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`H+ BC 9--!&;9C+&:@?@9H++!;P:9G>@=<!6#.!)'(0.2%0)#'(!&'3!K2-(0)#'(;! .9N+aH+ BC 3<@>+J:=I;G>A!&.-!KL;;! EC "&:-!05-!(023-'0(!+.-(-'0!05-).!+#(0-.(!&'3!6,&(5!%5&.0(!0#!05-!%,&((;! FC P(!05-!(023-'0(!&.-!+.-(-'0)'7!&(U!05-*!+-.0)'-'0!K2-(0)#'(!&(!&!.-:)-$;! .9N+]H+ BC EC FC HC !M&((!#20!!;P:9G>@=<+"?9EL9>@=<;! =5-!-K2&0)#'(!6#.!05-!2')0!*&/!#.!*&/!'#0!1-!+.#:)3-3;! =5-!`:&,2&0)#'!%&'!1-!%#2'0-3!&(!&!K2)@!#.!&!0-(0;! =5-!`:&,2&0)#'!(5#2,3!1-!7.&3-3!&0!05-!0-&%5-.G(!3)(%.-0)#'! )9>@=<9E+->9<K9:KAH+ !"#$%#$&'$(#)(*)&+Q!P(!&!.-(2,0!#6!&%0):)0)-(!)'!7.&3-(!aABE<!&,,!(023-'0(!(5#2,3!3-:-,#+Q! #!P1),)0)-(!'-%-((&./!0#!3#!(%)-'0)6)%!)'K2)./! #!I'3-.(0&'3)'7(!&1#20!(%)-'0)6)%!)'K2)./! !"#$%#$&'$(#)(*)&,Q!P(!&!.-(2,0!#6!&%0):)0)-(!)'!7.&3-(!aABE<!&,,!(023-'0(!(5#2,3!3-:-,#+!&'!2'3-.(0&'3)'7!#6Q! #!90.2%02.-!&'3!+.#+-.0)-(!#6!*&00-.! #!?'0-.&%0)#'(!#6!-'-.7/!&'3!*&00-.! ! !"#$%#$&'$(#)(*)&-Q!P(!&!.-(2,0!#6!&%0):)0)-(!)'!7.&3-(!aABE<!&,,!(023-'0(!(5#2,3!3-:-,#+!&'! 2'3-.(0&'3)'7!#6Q! #!9%)-'%-!&(!&!52*&'!-'3-&:#.! #!b&02.-!#6!(%)-'0)6)%!U'#$,-37-! /-+_H++1(&'()-+$).+#(!%"-!! &C !]1>-%0(!%5&'7-!05-).!*#0)#'!#',/!$5-'!&!'-0!6#.%-!)(!&++,)-3;!V&$(!#6!*#0)#'!&.-!2(-3!0#!%&,%2,&0-!+.-%)(-,/!05-! -66-%0(!#6!6#.%-(!#'!05-!*#0)#'!#6!#1>-%0(;!=5-!*&7')023-!#6!05-!%5&'7-!)'!*#0)#'!%&'!1-!%&,%2,&0-3!2()'7!05-! .-,&0)#'(5)+!W!c!*&<!$5)%5!)(!)'3-+-'3-'0!#6!05-!'&02.-!#6!05-!6#.%-;!S5-'-:-.!#'-!#1>-%0!-4-.0(!6#.%-!#'! &'#05-.<!&!6#.%-!-K2&,!)'!*&7')023-!&'3!#++#()0-!)'!3).-%0)#'!)(!-4-.0-3!#'!05-!6).(0!#1>-%0;!! 1C d.&:)0&0)#'!)(!&!2'):-.(&,!6#.%-!05&0!-&%5!*&((!-4-.0(!#'!&'/!#05-.!*&((;!=5-!(0.-'705!#6!05-!7.&:)0&0)#'&,! &00.&%0):-!6#.%-!1-0$--'!0$#!*&((-(!)(!+.#+#.0)#'&,!0#!05-!*&((-(!&'3!)':-.(-,/!+.#+#.0)#'&,!0#!05-!(K2&.-!#6! 05-!3)(0&'%-!1-0$--'!05-*;! /-+TH++%()-"!b$&'()+(#+")"!4c+$).+&0"+')%!"$-"+')+.'-(!."!!! 1CP,,!-'-.7/!%&'!1-!%#'()3-.-3!0#!1-!-)05-.!U)'-0)%!-'-.7/<!$5)%5!)(!05-!-'-.7/!#6!*#0)#'e!+#0-'0)&,!-'-.7/<! $5)%5!3-+-'3(!#'!.-,&0):-!+#()0)#'e!#.!-'-.7/!%#'0&)'-3!1/!&!6)-,3<!(2%5!&(!-,-%0.#*&7'-0)%!$&:-(;!! /-+`H++?)&"!$%&'()-+(#+")"!4c+$).+1$&&"!!! &C S&:-(<!)'%,23)'7!(#2'3!&'3!(-)(*)%!$&:-(<!$&:-(!#'!$&0-.<!&'3!,)750!$&:-(<!5&:-!-'-.7/!&'3!%&'!0.&'(6-.! -'-.7/!$5-'!05-/!)'0-.&%0!$)05!*&00-.! 1C `,-%0.#*&7'-0)%!$&:-(!.-(2,0!$5-'!&!%5&.7-3!#1>-%0!)(!&%%-,-.&0-3!#.!3-%-,-.&0-3;!`,-%0.#*&7'-0)%!$&:-(! )'%,23-!.&3)#!$&:-(!T05-!,#'7-(0!$&:-,-'705C<!*)%.#$&:-(<!)'6.&.-3!.&3)&0)#'!T.&3)&'0!5-&0C<!:)()1,-!,)750<! 2,0.&:)#,-0!.&3)&0)#'<!4A.&/(<!&'3!7&**&!.&/(;!=5-!-'-.7/!#6!-,-%0.#*&7'-0)%!$&:-(!)(!%&..)-3!)'!+&%U-0(!$5#(-! *&7')023-!)(!)':-.(-,/!+.#+#.0)#'&,!0#!05-!$&:-,-'705;!! %C `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d.&+5)%&,,/!%#*+&.-!&'3!&'&,/@-!3&0&!+#)'0(!&'3J#.!(2**&./!(0&0)(0)%(;! -; [-:-,#+!.-&(#'&1,-!%#'%,2()#'(!1&(-3!#'!3&0&!%#,,-%0-3;! 6; `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d.&+5)%&,,/!%#*+&.-!&'3!&'&,/@-!3&0&!+#)'0(!&'3J#.!(2**&./!(0&0)(0)%(;! [-:-,#+!.-&(#'&1,-!%#'%,2()#'(!1&(-3!#'!3&0&!%#,,-%0-3;! `:&,2&0-!$5-05-.!%#'%,2()#'(!&.-!.-&(#'&1,-!1/!.-:)-$)'7!05-!+.#%-((!&'3!%5-%U)'7!&7&)'(0!#05-.! &:&),&1,-!)'6#.*&0)#';! -%-B`W++->LK;<>A+S@EE+G=CCL<@G9>;+AG@;<>@P@G+@<?;A>@F9>@=<A+9<K+@<P=:C9>@=<+GE;9:ENW+ &; S.)0-!%,-&.<!%#5-.-'0!,&1#.&0#./!.-+#.0(!.-,&0-3!0#!(%)-'0)6)%!)':-(0)7&0)#'(;!! 1; S.)0-!%,-&.<!%#5-.-'0!&%%#2'0(!#6!%2..-'0!(%)-'0)6)%!)((2-(<!)'%,23)'7!+#(()1,-!&,0-.'&0):-!)'0-.+.-0&0)#'(!#6! 05-!3&0&;! %; I(-!3&0&!&(!-:)3-'%-!0#!(2++#.0!(%)-'0)6)%!&.72*-'0(!&'3!%,&)*(!)'!$.)00-'!#.!#.&,!+.-(-'0&0)#'(;! 3; M&.0)%)+&0-!)'!7.#2+!3)(%2(()#'(!#6!(%)-'0)6)%!)':-(0)7&0)#'!&'3!%2..-'0!(%)-'0)6)%!)((2-(;! -%-BdW+->LK;<>A+S@EE+;<B9<G;+:;9K@<F+@<+9EE+GL::@GLELC+9:;9A+DNH+! &;!D-&3)'7!)'!P,,!R2..)%2,2*!P.-&(!! f!D-&3!0-%5')%&,!0-40(!.-,&0-3!0#!:&.)#2(!(21>-%0!&.-&(!! %;!Z2),3)'7!:#%&12,&./!U'#$,-37-!! f![-*#'(0.&0-!&'!2'3-.(0&'3)'7!#6!%#'0-402&,!:#%&12,&./!)'!:&.)#2(!(21>-%0(;!! f!I(-!%#'0-'0!:#%&12,&./!)'!$.)0)'7!&'3!(+-&U)'7;! f!`4+,#.-!2'3-.(0&'3)'7!#6!'-$!$#.3(!6#2'3!)'!(21>-%0!&.-&!0-40(;!! 3;!`(0&1,)(5)'7!%#'0-40!! f!`4+,#.-!,)6-!-4+-.)-'%-(!.-,&0-3!0#!(21>-%0!&.-&!%#'0-'0;!! f![)(%2((!)'!1#05!$.)0)'7!&'3!(+-&U)'7!5#$!%-.0&)'!$#.3(!&.-!(21>-%0!&.-&!.-,&0-3;!! f![-0-.*)'-!(0.&0-7)-(!6#.!6)'3)'7!%#'0-'0!&'3!%#'0-402&,!*-&')'7!6#.!2'U'#$'!$#.3(;!! -/_W+->LK;<>A+S@EE+9<9EN\;+>B;+J:=J;:>@;A+9<K+9JJE@G9>@=<A+=P+S9?;AW+! &;!`4+,&)'!05-!+.#%-((-(!05&0!.-(2,0(!)'!05-!+.#32%0)#'!&'3!-'-.7/!0.&'(6-.!#6!-,-%0.#*&7'-0)%!$&:-(;!! 1;!`4+-.)*-'0&,,/!3-0-.*)'-!05-!1-5&:)#.!#6!$&:-(!)'!:&.)#2(!*-3)&!)'!0-.*(!#6!.-6,-%0)#'<!.-6.&%0)#'<!&'3! 3)66.&%0)#'!#6!$&:-(;!! %;!`4+,&)'!05-!.-,&0)#'(5)+!1-0$--'!05-!+5-'#*-'&!#6!)'0-.6-.-'%-!&'3!05-!+.)'%)+,-!#6!(2+-.+#()0)#';!! -;![-0-.*)'-!05-!,#%&0)#'!&'3!'&02.-!#6!)*&7-(!6#.*-3!1/!05-!.-6,-%0)#'!#.!.-6.&%0)#'!#6!,)750;!! -/7W+->LK;<>A+S@EE+9<9EN\;+>B;+:;E9>@=<AB@JA+D;>S;;<+P=:G;*+C9AA*+F:9?@>N*+9<K+>B;+C=>@=<+=P+=DI;G>AW+! 3;!g-&(2.-!&'3!%&,%2,&0-!05-!*&7')023-!#6!6.)%0)#'&,!6#.%-(!&'3!b-$0#'G(!05.--!V&$(!#6!g#0)#';!! -;!g-&(2.-!&'3!%&,%2,&0-!05-!*&7')023-!#6!7.&:)0&0)#'&,!6#.%-(;!! -/ZW+->LK;<>A+S@EE+;?9EL9>;+>B;+P=:CA+9<K+>:9<AP=:C9>@=<A+=P+;<;:FNW+! &;!P'&,/@-<!-:&,2&0-<!&'3!&++,/!05-!+.)'%)+,-!#6!%#'(-.:&0)#'!#6!-'-.7/!&'3!*-&(2.-!05-!%#*+#'-'0(!#6!$#.UA -'-.7/!05-#.-*!1/!! – f!3-(%.)1)'7!0#0&,!-'-.7/!)'!&!%,#(-3!(/(0-*;!! – f!)3-'0)6/)'7!3)66-.-'0!0/+-(!#6!+#0-'0)&,!-'-.7/;!! – f!%&,%2,&0)'7!U)'-0)%!-'-.7/!7):-'!*&((!&'3!:-,#%)0/;!! – f!.-,&0)'7!0.&'(6#.*&0)#'(!1-0$--'!+#0-'0)&,!&'3!U)'-0)%!-'-.7/;!! 1;!`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e+Gf?e!%!c!F!`!h!*J(;!!=#!%&,%2,&0-!05-!&%02&,!&*#2'0!05&0!&!,)750!.&/!$),,!1-'3!%&'! ! @Q+e+<:MA@<! ! :Q;!!! 1-!3-0-.*)'-3!1/!-<;EEgA+,9SH++<@MA@<! @+:;J:;A;<>A+>B;+@<G@K;<>+=:+ @<G=C@<F+:9N+9<K+:+:;J:;A;<>A+ >B;+:;P:9G>;K+:9N 500+QJJ$$$;+5/()%(%,&((.##*;%#*JR ,&((J.-6.'JIBH,E&;%6*! ! + ! + ]1>-%0(!&++-&.!0#!1-!)'!3)66-.-'0!+#()0)#'(!32-!0#!.-6.&%0)#';!!=5)(!)(!05-!.-&(#'!$5/!&!+-''/!#'!05-!1#00#*!#6! 05-!+##,!&++-&.(!%,#(-.!05&'!)0!&%02&,,/!)(;!!=#!%&,%2,&0-!05-!&++&.-'0!#.!&%02&,!5-)750!T#.!3-+05C!05-!-K2&0)#'! BgfB+e+<:f<@!%&'!1-!2(-3;!!"G!c!&++&.-'0!5-)750<!5!c!&%02&,!5-)750<!'.!c!)'3-4!6#.!.-6.&%0):-!*&0-.)&,!TE'3! *-3)2*C<!&'3!')!c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f+<@O+P=:+<@+h+<:;! ^;P=:;+>B;+G:@>@G9E+9<FE;+>B;+E@FB>+S@EE+:;P:9G>+>B:=LFB+ >B;+<;i>+C;K@9O+9>+>B;+G:@>@G9E+9<FE;+>B;+E@FB>+:9N+S@EE+ >:9?;E+J9:9EE;E+>=+>B;+D=L<K9:NW++$<N+E@FB>+:9N+S@>B+9<+ @<G@K;<>+9<FE;+E9:F;:+>B9<+>B;+G:@>@G9E+9<FE;+S@EE+D;+ >=>9EEN+@<>;:<9EEN+:;PE;G>;K+9>+>B;+D=L<K9:NW+ 500+QJJ$$$;+5/()%(%,&((.##*;%#*JR,&((J.-6.'JIBH,F1;%6*! ! ! ]'-!&++,)%&0)#'!#6!0#0&,!)'0-.'&,!.-6,-%0)#'!)(!)'!6)1-.!#+0)%(;!!d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i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j+%=<?;iQ+ Ray Parallel ray Central ray Focal ray ! From object to lens Parallel to principal axis To the center of the lens Passes through focal point, F From lens to image Passes through focal point, F From the center of the lens Parallel to principal axis !LE;A+P=:+.:9S@<F+!;P;:;<G;+!9NA+M.@?;:F@<F+E;<A+j+%=<G9?;Q+ Ray Parallel ray Central ray Focal ray From object to lens Parallel to principal axis To the center of the lens Proceeding toward back focal point, F From lens to image Directed away from focal point, F From the center of the lens Parallel to principal axis ! 500+QJJ$$$;+5/()%(%,&((.##*;%#*JR,&((J.-6.' JIBH,L1;%6*! ! ! =5-!,-'(!-K2&0)#'(!&.-Q!!7fJ+[+7fk+e+7fP+9<K+1+e+2kfJ+e+BgfB! +!c!#1>-%0!3)(0&'%-! K!c!)*&7-!3)(0&'%-! 6c!6#%&,!,-'705! !!!!!!g!c!*&7')6)%&0)#'!! !!!5G!c!)*&7-!50;!!!!!!5!c!#1>-%0!50;! R#':-.7)'7!TR#':-4C!V-'(Q!!i6! ! [):-.7)'7!TR#'%&:-C!V-'(Q!A6! )6!K!)(!'-7&0):-!)0!)(!&!:).02&,!)*&7-!)6!)0!)(!+#()0):-!)0!)(!&!.-&,!)*&7-! )6!g!#.!5G!&.-!'-7&0):-!05-'!05-!)*&7-!)(!)':-.0-3!)6!05-/!&.-!+#()0):-!05-'!05-!)*&7-!)(!2+.)750! )6!g!)(!7.-&0-.!05&'!#'-!05-!)*&7-!)(!*&7')6)-3!)6!)0!)(!,-((!05&'!#'-!05-'!05-!)*&7-!)(!.-32%-3! %=<?;:F@<F+M%=<?;iQ+,;<A;A+G9<+D;+ :;9E+=:+?@:>L9EO+LJ:@FB>+=:+@<?;:>;KO+ 9<K+:;KLG;K*+C9F<@P@;K*+=:+>B;+ A9C;+A@\;+9A+>B;+=DI;G>W!!!&B;A;+ E;<A;A+9:;+LA;K+@<+C9F<@PN@<F+ FE9AA;A*+C@G:=AG=J;A+9<K+:;P:9G>@<F+ >;E;AG=J;AW++&B;N+9EA=+G9<+G=::;G>+ P9:A@FB>;K+MBNJ;:=J@9Q+?@A@=<W! 500+QJJ(3(2A +5/()%(;#.7J+5/()%(Bh_J+5/()%(Bh_ZJ= #+)%(J,)750J)*&7-(j,)750J%5EHj,-'(j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bC!32-!0#!05-! :;P:9G>@?;+@<K;i+M<+e+Gf?Q+3)66-.-'%-!1-0$--'!&!K@;E;G>:@G!#1>-%0!&'3!)0(!(2..#2'3)'7!*-3)2*!0#!+5/()%&,,/!5#,3!&'3! *#:-!05-!#1>-%0;!!!?6!05-!+&.0)%,-!)(!,&.7-.!05&'!05-!$&:-,-'705!#6!05-!,&(-.!2(-3!05-'!.&/!#+0)%(!%&'!1-!2(-3!0#!3-(%.)1-! 5#$!05-!]=(!$#.U;!!P(!&!d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e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h+#AG9>>;:@<F+(#!05-/!&.-!0.&++-3!)'!05-!.-7)#'!'-&.!05-!6#%2(;!!T=5-.-!&.-! #05-.!6#.%-(!(2%5!&(!7.&:)0/!)':#,:-3!120!05-(-!&.-!%#*+&.&0):-,/!(*&,,;C! r!![).-%0)#'! 500+QJJ$$$;(0A &'3.-$(;&%;2UJ(--)'7,)6-J(%)-' %-J.-(-&.%5J0.&++)'7J0.&++)'7; 50*,! ! ! ! ]+0)%&,!,&(-.(!&.-!2(-3!)'!*&'/!(%)-'0)6)%!.-(-&.%5!&.-&(;!!W#.!-4&*+,-<!05-/!&.-!2(-3!0#!0.&+!3)-,-%0.)%!(+5-.-(<!1&%0-.)&<! :).2(-(<!%-,,(<!#.7&'-,,-(!&'3!(0.&'3(!#6![bP;!!Z/!0.&++)'7!05-(-!+&.0)%,-(!05-/!%&'!1-!%#'6)'-3<!#.7&')@-3<!0.&%U-3<! *-&(2.-3!&'3!-:-'!&,0-.-3;!!=$#!*&)'!2(-(!6#.!]=(!5&:-!1--'!)'!05-!(023/!#6!*#,-%2,&.!*#0#.(!T-4Q!!U)'-()'<!*/#()'<! -0%;C!&'3!05-!+5/()%&,!&(+-%0(!#6![bP;!!S)05!1#05!(023)-(!&!1)#,#7)%&,!(+-%)*-'!)(!1)#%5-*)%&,,/!&00&%5-3!0#!&!3)-,-%0.)%! +&.0)%,-!T*)%.#'!()@-3C!&'3!+.#+-.0)-(!T!6#.!-4&*+,-Q!!-,&(0)%)0/<!6#.%-(<!(0-+!()@-<!-0%;C!#6!05-(-!(21>-%0(!%&'!1-!(023)-3;! !;P;:;<G;AH+ • 9-.$&/<!D&/*#'3!P;<!&'3!k-../!9;!W&275';!!"#,0!M5/()%(;!!P2(0)'<!=-4&(Q!!"#,0<!D)'-5&.0!&'3!S)'(0#'<!E___;! • XD-6.&%0)#'!&'3!D&/!g#3-,!#6!V)750Y;!!=5-!M5/()%(!R,&((.##*;!l!BaaNAE_B_!=5-!M5/()%(!R,&((.##*<!P,,!.)750(! .-(-.:-3;!%#*MP[D`;!!k2'-!Bh<!E_B_;!m500+QJJ$$$;+5/()%(%,&((.##*;%#*JR,&((J.-6.'Jn! • o')750<!P,-4e!g&(5&'#:<!d.-7#./e!g#,,#/<!k2(0)';XP!Z.)-6!")(0#./!#6!]+0)%&,!=$--@-.(Y;!!!"#$%&'()%&*+%&' (&,-+.&/�-',#1'2")%)$"*,%'()0).-;!![-+&.0*-'0!#6!Z)#,#7/<!I'):-.()0/!#6!p#.U;!!P%%-((-3!k2'-!EF<!E_B_;! m500+QJJ$$$E;1)#%5;#4;&%;2UJq#21(2J-1>U')750J0)*-,)'-;50*,n! • X]+0)%&,!=$--@-.(Y;!!3"4"5&1",;!!k2'-!E_<!E_B_;!S)U)*-3)&!W#2'3&0)#'<!?'%;!!P%%-((-3!k2'-!EH<!E_B_;! m500+QJJ-';$)U)+-3)&;#.7J$)U)J]+0)%&,j0$--@-.(n! • [--(#'<!`.)%;TE__OC;!6)%%"#-'7#0&.#&089"#4&1':"*0")#,.;')<'=>;-"*-;!V#'3#'Q!!"&.+-.R#,,)'(!=+?%"->&.-!V03;! • X]+0)%&,!=.&++)'7Q!!"#$!3#-(!)0!S#.U8Y;!!!&&"#$'9"<&'@>.)+$>','A&B'9"$>0C''=>)0)#"*-'<).'D&,%0>*,.&',#1' (&1"*"#&;!9%5##,!#6!M5/()%(!&'3!P(0.#'#*/<!I'):-.()0/!#6!90;!P'3.-$(;!!`'7)'--.)'7!&'3!M5/()%(!9%)-'%-(! D-(-&.%5!R#2'%),;!P%%-((-3!k2'-!EE<!E_B_;!m500+QJJ$$$;(0A &'3.-$(;&%;2UJ(--)'7,)6-J(%)-'%-J.-(-&.%5J0.&++)'7J0.&++)'7;50*,n! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! • M#.0-.A[&:)(<!o&.-';!!?'0-.:)-$!$)05![.;!k-'')6-.!R2.0)(;![-+&.0*-'0!#6!M5/()%(;!d-#.7)&!?'(0)020-!#6!=-%5'#,#7/;!! P0,&'0&<!d-#.7)&;!H!k2'-!E_B_;! • M#.0-.A[&:)(<!o&.-';!!R#'0)'2#2(!)'0-.:)-$!$)05!V#2)(!g%V&'-;![-+&.0*-'0!#6!M5/()%(;!d-#.7)&!?'(0)020-!#6! =-%5'#,#7/;!!P0,&'0&<!d-#.7)&;!92**-.!E_B_;! + !"#!$%&'()+."1()-&!$&'()-+ + '<K;i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`4+,&)'!0#!05-! %,&((!05&0!()'%-!05-!S&.1,-00-(\!&'3!$&0-.!5&:-!05-!(&*-!)'3-4!#6!.-6.&%0)#'!05-.-!)(!'#!1-'3)'7!#6!,)750!&'3! 05-.-6#.-!'#!$&/!0#!3)(%-.'!1-0$--'!05-!0$#!*&0-.)&,(;! ! =5)(!)3-&!%&'!&,(#!1-!3-*#'(0.&0-3!$)05!M/.-4\!&'3!,)750!:-7-0&1,-!#),;!!=&U-!&!,&.7-<!%,-&'!1-&U-.!&'3!+,&%-!&! ,#'7<!%,-&'!M/.-4\!0-(0!021-!T#.!#05-.!%#'0&)'-.C!)'()3-!05-!1-&U-.;!!W),,!05-!1-&U-.!$)05!:-7-0&1,-!#),!T"FJH05! 62,,C!&'3!05-'!(,#$,/!+#2.!05-!:-7-0&1,-!#),!)'0#!05-!0-(0!021-;!!"&:-!05-!(023-'0(!$&0%5!%&.-62,,/!&(!05-!0-(0! 021-!(0&.0(!0#!3)(&++-&.!$)05)'!05-!1-&U-.;! ! #@D;:+(J>@GA+.;C=H!!=&U-!&!,&(-.!&'3!(5)'-!)0!&0!#'-!-'3!#6!&!W)1-.!]+0)%(!=21-;!!M#)'0!#20!0#!05-!(023-'0(! 05&0!05-!,&(-.!(0&/(!$)05)'!05-!021-!-:-'!05.#275!,##+(!&'3!%2.:-(;!!"&:-!05-!(023-'0(!&00-*+0!0#!-4+,&)'!$5/! 05-!,&(-.!$),,!3#!05)(!)'!05-!6)1-.!#+0)%!021-!120!3#-(!'#0!1-'3!&.#2'3!05-!%#.'-.!$5-'!)0!(5#'-!#20!05-! 3##.$&/;!!=5-/!(5#2,3!3-(%.)1-!05-!%#'%-+0!#6!0#0&,!)'0-.'&,!.-6,-%0)#';! ! .@AJ;:A@=<+.;C=H!!95)'-!&!$5)0-!,)750!(#2.%-!05.#275!&!+.)(*!#'0#!&!$5)0-!1&%U7.#2'3;!!"&:-!05-!(023-'0(! 3-(%.)1-!$5&0!05-/!(--!T&!.&)'1#$C!&'3!$5&0!5&(!5&++-'-3!0#!05-!,)750!&(!)0!$-'0!05.#275!05-!+.)(*!&'3!$5/! T05-!%#,#.(!#6!05-!:)()1,-!(+-%0.2*!(-+&.&0-3!#20!32-!0#!05-).!$&:-,-'705(;!!=5-!,#'7-.!05-!$&:-,-'705!05-! ,-((!05-!,)750!$),,!.-6.&%0;!!! ! ! ,;<A+$G>@?@>NH!!M&((!#20!&!:&.)-0/!#6!3)66-.-'0!()@-!,-'(-(!&'3!5&:-!05-!(023-'0(!,##U!05.#275!05-*!&0! 3)66-.-'0!3)(0&'%-(;!!"&:-!05-*!3-0-.*)'-!$5)%5!&.-!%#':-4!&'3!$5)%5!&.-!%#'%&:-!,-'(-(;! !"#!$%&'()+!"b'"X+/!(l"%&+ '<A>:LG>@=<AH+++ c=L+9:;+>=+G:;9>;+9+#E9AB+%B9:>+M$+B;9?N2KL>N+J9J;:+<=>;D==Y+@<A;:>Q+=:+/=A>;:+9A+9+:;?@;S+ FL@K;+P=:+!;P:9G>@=<*+,;<A;A+9<K+(J>@G9E+/B;<=C;<=<W++&B@A+J:=I;G>+S@EE+D;+KL;+=<+ mmmmmmmmmmmmmmmmmmmmmmW++&B;:;+S@EE+D;+9+76+J>+K;KLG>@=<+P=:+;?;:N+AGB==E+K9N+>B;+J:=I;G>+ @A+E9>;+S@>B=L>+J:=J;:+;iGLA;W+ + &B;+#E9AB+%B9:>f/=A>;:+AB=LEK+@<GELK;H+ 9Q $+>@>E;+9<K+9+D:@;P+=?;:?@;S+=P+>B;+;<>@:;+L<@>W+ + DQ .@?@A@=<A+P=:+;9GB+A;G>@=<+M>B:;;+A;G>@=<AH+!;P:9G>@=<*+,;<A;A+9<K+(J>@G9E+ /B;<=C;<=<Q++@<+>B;+L<@>W+ + GQ "9GB+A;G>@=<+K@?@A@=<+AB=LEK+@<GELK;H+ + 7Q &B;+A;G>@=<+=DI;G>@?;A+MALCC9:NQ+ + 5Q $EE+@CJ=:>9<>+>;:CA+9<K+>B;@:+K;P@<@>@=<A+ + ZQ $EE++;kL9>@=<A+LA;K+@<+>B;+A;G>@=<+S@>B+;i9CJE;+J:=DE;CA+P=:+;9GB+ + _Q $>+E;9A>+>S=+?@AL9EA+MGB9:>A*+F:9JBA*+K@9F:9CA*+J@G>L:;A*+;>GWQ+>B9>+:;E9>;+>=+ >B;+A;G>@=<W+ + KQ++$EE+#E9AB+%B9:>A+AB=LEK+D;+>NJ;K+M=<EN+;iG;J>@=<+j+>B;+G9EGLE9>@=<AQ+9<K+JE9G;K+=<+ G=E=:;K+J9J;:+M<=+<=>;D==Y+J9J;:QW++/=A>;:A+G9<+D;+K;A@F<;K+=<+J=A>;:+D=9:K+=:+ >B:=LFB+>B;+S;DA@>;+http://edu.glogster.com+W++%=<>;<>+kL9E@>N*+:;9K9D@E@>N+ M=:F9<@\9>@=<Q*+<;9><;AA+9<K+G:;9>@?@>N+S@EE+9EE+D;+G=<A@K;:;KW+ + #,$-0+%0$!&+!3^!'%+ )9C;H++mmmmmmmmmmmmmmmmmmmmmmmmmmm+.9>;H++mmmmmmmmmmmmm+/;:@=KH++mmmmm+ + 0 No Title 2 NonRelevant Title 3 5 TITLE OF Appropriate Appropriate Title Given CHAPTER/TOPIC Title Given with Grammatical Errors 0-3 4-6 8 10 Clear, Clear, SYNOPSIS OF Requirement Unorganized Concise Concise with/without CHAPTER/TOPIC not Synopsis Synopsis Grammatical Met/Very with no with a few Errors Unorganized Grammatical Grammatical with Errors Errors Grammatical Errors 0-6 8 - 12 14 -18 20 All Section At least 75 SECTION Requirement 50 – 74% of Objectives % of Section Section OBJECTIVES not Met/Less Answered Objectives Objectives than 50% of Correctly Answered Answered Section Correctly Correctly Objectives Answered Correctly 0-3 4-6 7-9 10 All Terms At least 75 IMPORTANT Requirement 50 – 74% of Defined % Terms Terms TERMS not Met/Less Correctly Defined Defined than 50% of Correctly Correctly Terms Defined Correctly 0-3 4-6 7-9 10 All At least 75 EQUATIONS Requirement 50 – 74% of Equations % Equations Equations not Met/Less Defined Defined Defined than 50% of Correctly Correctly Correctly Equations Defined Correctly SECTION VISUALS TYPED FLASH CHARTS 0-3 Missing More than 4 Meaningful Visuals 0-3 Requirement not Met/Less than 75% of Flash Chart is Typed (sans calculation) 4 CONTENT Content QUALITY Quality is Poor 4 ORGANIZATION/ Majority of NEATNESS Flash Chart is Unorganized CREATIVITY/ PERCEIVED EFFORT 1 Very Little Perceived Effort 4-5 Missing 3-4 Meaningful Visuals 7-8 Missing 1-2 Meaningful Visuals 4-6 At least 75 % of Flash Chart is Typed (sans calculations) 8 All of the Flash Chart is Typed (messy calculations) 10 At least Two Meaningful Visuals for Each Section 10 All of the Flash Chart is Typed (sans calculations but they are written neatly) 10 Content Quality is Excellent 10 Flash Chart is Very Organized 6 8 Content Content Quality is Quality is Satisfactory Very Good 6 8 Flash Chart Some is Organized Sections of the Flash Chart are Unorganized 2 3 5 Meaningful Some Creative Creative Perceived Touches Touches Effort Were Added/ Were Added/ Some A lot of Perceived Perceived Effort Effort + + ^=<LA+/=@<>AH++mmmmmmmmmmmmmmmmmmmmmm+ + + &=>9E+-G=:;H++mmmmmmmmmmmmmmmmmmmmmmm+ RUBRIC FOR POSTER/BROCHURE/VIDEO/COMIC BOOK Name(s): _____________________________ Project: _________________ Period(s): ____ CRITERIA QUALITY OF INFORMATION VISUAL NEATNESS AND ORGANIZATION CREATIVITY TECHNICAL ASPECTS (GRAMMAR/SPELLING, ETC.) REFERENCES POINTS 0-11 Information does not relate to the task and is difficult to follow. 12-17 Information is somewhat related to the task. 0-11 Project is very messy and unorganized. Very little effort is perceived. 12-17 Project is a little messy and/or unorganized. Some effort is perceived. 0-3 Project shows no creative thought in presentation. 4-9 Project displays some creative thought. 0-4 Many technical mistakes (more than three). 5-7 Two to three technical mistakes. 0 No references 4-7 Some type of reference and documentation. 18-23 Information presented is relative to task and information is somewhat easy to understand. 18-23 Project is fairly neat and organized. A good amount of effort is perceived. 10-15 Project is creative and relevant to the task. (Creative Flare) 8 One technical mistake. 24-30 Information presented is very relative to task and information is very easy to understand. 24-30 Project is very neat and organized. A great deal of effort is perceived. 16-20 Very creative and relevant to the task. A very unique presentation. 10 No technical mistakes. 8 At least two quality references. 10 At least two quality references documented correctly. Total Points: ______________/100 Teacher Comments: REFRACTION AND OPTICAL PHENOMENA WORKSHEET Name: ______________________________ Date: ____________ Period: _______ 1. What is the velocity of light in a polystyrene bead (n = 1.49)? 2. What is the index of refraction of an unknown liquid if the speed of light through the liquid is 1.999 E 8 m/s? 3. Find the angle of refraction for a ray of light that enters cubic zirconia (n = 2.20) from glycerine (n = 1.473) at an angle of 26o to the normal. 4. A ray of light traveling in air enters a slab of transparent material. The incoming ray makes an angle of 53o with the normal, and the refracted ray makes an angle of 33o with the normal. Find the index of refraction of the transparent material. 5. A snorkeler under water looks up and sees a bird flying above the water. The bird appears to be 2 meters above the water. What is the actual location of the bird? 6. A 9 cm thick glass block (n = 1.5) lies on top of a stamp. How thick does the glass block appear to be? 7. What is the critical angle of light traveling through ice (n = 1.309) into air? 8. The critical angle of an unknown liquid mixed with water (n = 1.333) is 55o. What is the unknown liquid’s index of refraction? 9. A) After a storm, a man walks out onto his porch. Looking to the east, he sees a rainbow that has formed above his neighbor’s house. What time of day is it, morning or evening? B) Why does the arc of a rainbow appear with red colors on top and violet colors on the bottom? 10. What are the conditions necessary for the occurrence of a mirage? ! ! ANSWER KEY: REFRACTION AND OPTICAL PHENOMENA WORKSHEET Name: ______________________________ Date: ____________ Period: _______ 1. What is the velocity of light in a polystyrene bead (n = 1.49)? n = c/v ! v = (3 E 8 m/s) / (1.49) = 2 E 8 m/s 2. What is the index of refraction of an unknown liquid if the speed of light through the liquid is 1.999 E 8 m/s? n = c/v ! (3 E 8 m/s) / (1.999 E 8 m/s) = 1.5 3. Find the angle of refraction for a ray of light that enters cubic zirconia (n = 2.20) from glycerine (n = 1.473) at an angle of 26o to the normal. ! i) = nr(sin! ! r) ! 1.473 (sin 26º) = 2.20(sin! ! r) ! (sin! ! r) = (0.646)/2.20 ! ! r = sin-1 (0.294) = ni (sin! 17o 4. A ray of light traveling in air enters a slab of transparent material. The incoming ray makes an angle of 53o with the normal, and the refracted ray makes an angle of 33o with the normal. Find the index of refraction of the transparent material. ni (sin! ! i) = nr(sin! ! r) ! 1 (sin 53º) = nr(sin33o) ! nr = (0.799) / 0.545 = 1.45 5. A snorkeler under water looks up and sees a bird flying above the water. The bird appears to be 2 meters above the water. What is the actual location of the bird? h’/h = nr/ni ! 2 m/h = 1.333/1 ! h = 2 m/1.333 = 1.5 m 6. A 9 cm thick glass block (n = 1.5) lies on top of a stamp. How thick does the glass block appear to be? h’/h = nr/ni ! h’/9 cm = 1/1.5 ! h’ = 6 cm 7. What is the critical angle of light traveling through ice (n = 1.309) into air? sin! ! c = nr/ni ! sin! ! c = 1/1.309 ! ! c = sin-1(0.764) ! 49.8o 8. The critical angle of an unknown liquid mixed with water (n = 1.333) is 55o. What is the unknown liquid’s index of refraction? sin! ! c = nr/ni ! sin 55o = nr/1.333 ! nr = 1.09 9. A) After a storm, a man walks out onto his porch. Looking to the east, he sees a rainbow that has formed above his neighbor’s house. What time of day is it, morning or evening? Evening, since the sun rises in the east and sets in the west and because the sun must be behind him to see the rainbow B) Why does the arc of a rainbow appear with red colors on top and violet colors on the bottom? Violet light is bent more than red light as it passes through the drops of water due to their wavelengths 10. What are the conditions necessary for the occurrence of a mirage? Inferior: The air next to the ground must be hotter than the air above it. Superior: The air next to the water must be cooler than the air above it (and the object must be past the horizon).! ! ! REFRACTION AND LENSES WORKSHEET Name: _____________________________ Date: ____________ Period: _____ 1. An object is placed 16 cm in front of a converging lens of focal length 9 cm. Find the image distance and the magnification. Describe the image. 2. An object is placed 6 cm in front of a converging lens of focal length 12 cm. Find the image distance and the magnification. Describe the image. 3. An object is placed 15 cm in front of a converging lens of focal length 5 cm. Find the image distance and the magnification. Describe the image. 4. An object is placed 7 cm in front of a diverging lens of focal length 10 cm. Find the image distance and the magnification. Describe the image. 5. A diverging lens is used to form a virtual image of an object. The object is 80 cm in front of the lens, and the image is 40 cm in front of the lens. Determine the focal length of the lens. 6. Where must an object be placed to have a magnification of 3.00 in a diverging lens of focal length 11 cm? 7. In order to get an upright image, slides must be placed upside down in a slide projector. What type of lens must the slide projector have? Is the slide inside or outside the focal point of the lens? 8. Sherlock Holmes examines a clue by holding his magnifying glass (with a focal length of 15 cm) 8 cm away from an object. Find the image distance and the magnification. Describe the image that he observes. ! ! ! ! ! ! ! ! ! ANSWER KEY: REFRACTION AND LENSES WORKSHEET Name: _____________________________ Date: ____________ Period: _____ 1. An object is placed 16 cm in front of a converging lens of focal length 9 cm. Find the image distance and the magnification. Describe the image. 1/p + 1/q = 1/f ! q = (1/9 cm – 1/16 cm)-1 ! q = +20.57 cm M = -q/p ! - (+20.57 cm)/(16 cm) = - 1.3 Real, inverted, magnified 2. An object is placed 6 cm in front of a converging lens of focal length 12 cm. Find the image distance and the magnification. Describe the image. 1/p + 1/q = 1/f ! q = (1/12 cm – 1/6 cm)-1 ! q = -12 cm M = -q/p ! - (-12 cm)/(6 cm) ! +2 Virtual, upright, magnified 3. An object is placed 15 cm in front of a converging lens of focal length 5 cm. Find the image distance and the magnification. Describe the image. 1/p + 1/q = 1/f ! q = (1/5 cm – 1/15 cm)-1 ! +7.5 cm M = -q/p ! - (+7.5 cm)/(15 cm) = - 0.5 Real, inverted, reduced 4. An object is placed 7 cm in front of a diverging lens of focal length 10 cm. Find the image distance and the magnification. Describe the image. 1/p + 1/q = 1/f ! q = (-1/10 cm – 1/7 cm)-1 ! -4.12 cm M = -q/p ! - (-4.12 cm)/(7 cm) = + 0.59 Virtual, upright, reduced 5. A diverging lens is used to form a virtual image of an object. The object is 80 cm in front of the lens, and the image is 40 cm in front of the lens. Determine the focal length of the lens. 1/p + 1/q = 1/f ! f = (1/80 cm + (-1/40 cm))-1 = - 80 cm 6. Where must an object be placed to have a magnification of 3.00 in a diverging lens of focal length 11 cm? A diverging lens cannot form an image larger than the object 7. In order to get an upright image, slides must be placed upside down in a slide projector. What type of lens must the slide projector have? Is the slide inside or outside the focal point of the lens? Converging lens (diverging only give upright); outside (if inside the image is virtual) 8. Sherlock Holmes examines a clue by holding his magnifying glass (with a focal length of 15 cm) 8 cm away from an object. Find the image distance and the magnification. Describe the image that he observes. ! A magnifying glass is a converging lens; 1/p + 1/q = 1/f ! q = (1/15 cm – 1/8 cm)-1 ! q = -17.1 cm M = -q/p ! - (-17.1 cm)/(8 cm) ! +2.1 Virtual, upright, magnified ! ! TEAM TRIVIA: REFRACTION Instructions: Divide class into groups of 3 or 4. Pass out 4 note cards (with letters A, B, C, and D on one card each) to each group. Allow students to use scrap paper and calculators. You may provide equations to each group as well. Read the question and all the choices allowed to the class and let each group send up a representative with their answer. Every group should get a chance to answer (this is not a first come first served game). At the end of the multiple choice round pass out the Bonus Round Sheet to each group to work on (you may establish an appropriate time limit). Tally up each groups’ points. I usually give 1st place 6 pts on their evaluation, 2nd place 5 pts, etc. (you can award your winners any way that you like. 7W $+:9N+=P+E@FB>+@<+9@:+@A+@<G@K;<>+=<+9<+9@:2>=2FE9AA+D=L<K9:N+9>+9<+9<FE;+=P+;i9G>EN+Z6°° +S@>B+>B;+<=:C9EW++ 'P+>B;+@<K;i+=P+:;P:9G>@=<+=P+>B;+FE9AA+@A+7W`T*+SB9>+@A+>B;+9<FE;+=P+>B;+:;P:9G>;K+:9N+S@>B@<+>B;+FE9AA+ S@>B+:;AJ;G>+>=+>B;+<=:C9En+ + 9Q T`°° + DQ _`°° + GQ 5d°° + KQ 7]°° + + 5W +XB;<+E@FB>+J9AA;A+>B:=LFB+9+J:@AC+SB@GB+G=E=:+=P+>B;+AJ;G>:LC+D;<KA+>B;+E;9A>n+ + 9Q b@=E;>+ DQ 4:;;<+ GQ c;EE=S+ KQ (:9<F;+ + ZW XB@GB+@A+<=>+9+G=<K@>@=<+>B9>+CLA>+D;+C;>+P=:+:;P:9G>@=<+>=+=GGL:n+ + 9Q ! @+o+6+ DQ ! @+e+! ! :++ GQ <@+o+<:+ KQ D=>B+C;K@9+CLA>+D;+>:9<AJ9:;<>+ + _W +$+GLD;+=P+;KF;+`+GC+@A+JE9G;K+=?;:+9+J:@<>;K+J9F;W+$>+SB9>+K@A>9<G;+P:=C+>B;+>=J+AL:P9G;+=P+>B;+GLD;+ S@EE+>B;+E;>>;:A+9JJ;9:+SB;<+A;;<+P:=C+9D=?;n+!;P:9G>@?;+@<K;i+=P+FE9AA+e+7WTW+ + 9Q 6W5T+GC+ DQ d+GC+ GQ _+GC+ KQ 6W77+GC+ + + + + TW $<+=DI;G>+@A+JE9G;K+56+GC+@<+P:=<>+=P+9+K@?;:F@<F+E;<A+=P+P=G9E+E;<F>B+76+GCW++#@<K+>B;+@C9F;+K@A>9<G;+ 9<K+>B;+C9F<@P@G9>@=<W+ + 9Q [56+GCO+27+ DQ 2`W`a+GCO+[6WZZZ+ + GQ 256+GCO+[7+ KQ [`W`a+GCO+26WZZZ+ + `W &B@A+@A+>B;+C=A>+G=CC=<+C@:9F;W++,@FB>+:9NA+P:=C+>B;+AYN+9:;+:;P:9G>;K+9<K+>B;+=DA;:?;:+A;;A+>B;+ @C9F;+=P+>B;+AYN+>L:<;K+LJA@K;2K=S<W+ + 9Q '<P;:@=:+C@:9F;+ DQ -LJ;:@=:+C@:9F;+ GQ -@<Y@<F+C@:9F;+ KQ &=S;:@<F+C@:9F;+ + aW XB9>+>NJ;+=P+@C9F;+@A+J:=KLG;K+DN+>B;+G=:<;9+9<K+>B;+E;<A+=<+>B;+:;>@<9n+ + 9Q b@:>L9E*+@<?;:>;K+ DQ b@:>L9E*+LJ:@FB>+ GQ !;9E*+LJ:@FB>+ KQ !;9E*+@<?;:>;K+ + ]W $<+L<K;A@:9DE;+;PP;G>+@<+SB@GB+9<+=DI;G>+?@;S;K+>B:=LFB+9+E;<A+9JJ;9:A+>=+D;+:@<F;K+S@>B+G=E=:+@A+ mmmmmmmmmmmmmmmmmmmmW+ + 9Q %B:=C9>=F:9JB+ DQ $GB:=C9>@G+E;<A+ GQ %B:=C9>@G+9D;::9>@=<+ KQ %B:=C9>@G+AJ;GLE9>@=<+ + dW #@<K+>B;+G:@>@G9E+9<FE;+P=:+E@FB>+>:9?;E@<F+P:=C+@G;+M<+e+7WZ6dQ+@<>=+9@:W+ + 9Q _dW]=+ DQ d6=+ GQ 7WZ=+ KQ >B;:;+@A+<=+G:@>@G9E+9<FE;+ + 76W $<+=DI;G>+@A+JE9G;K+9E=<F+>B;+J:@<G@J9E+9i@A+=P+9+>B@<+K@?;:F@<F+E;<A+>B9>+B9A+9+P=G9E+J=@<>+=P+55+GCW++'P+ >B;+K@A>9<G;+P:=C+>B;+=DI;G>+>=+>B;+E;<A+@A+Z`+GC*+SB9>+@A+>B;+K@A>9<G;+P:=C+>B;+@C9F;+>=+>B;+E;<An+ + 9Q Ta+GC+ DQ j6W6a+GC+ GQ j7ZW`+GC+ KQ 6W65+GC+ + !"#!$%&'()+^()3-+!(3).+ 4:=LJ+1;CD;:+)9C;AH+mmmmmmmmmmmmmmmmmmmmmmmmmmmmm+.9>;H++mmmmmmmmm/;:@=KH++mmmm+ 4:=LJ+pH++mmmmmmmmm+ 7W XB9>+@A+>B;+)=:C9E+E@<;n+++ + + 5W XB;<+K=;A+E@FB>+D;<K+>=S9:KA+>B;+<=:C9En+ + + ZW XB9>+@A+>B;+AJ;;K+=P+E@FB>+@<+S9>;:n+ + + _W $+P:@;<K+>B:=SA+9+G=@<+@<>=+9+J==EW++c=L+GE=A;+N=L+;N;A+9<K+K@?;+>=S9:K+>B;+AJ=>+SB;:;+N=L+A9S+@>+ P:=C+>B;+;KF;+=P+>B;+J==EW++XB;<+N=L+:;9GB+>B;+D=>>=C*+S@EE+>B;+G=@<+D;+@<+P:=<>+=P+N=L+=:+D;B@<K+ N=Ln+ + + + TW #@<K+>B;+@C9F;+J=A@>@=<+9<K+>B;+C9F<@P@G9>@=<+P=:+9<+=DI;G>+JE9G;K+Z+GC+=L>A@K;+>B;+P=G9E+J=@<>+=P+9+ G=<?;:F@<F+E;<A+S@>B+9+_+GC+P=G9E+E;<F>BW++.;AG:@D;+>B;+@C9F;W+ + + + + `W -LJJ=A;+9+J9<;+=P+PE@<>+FE9AA*+S@>B+9+:;P:9G>@?;+@<K;i+=P+7W`T*+@A+@CC;:A;K+@<+S9>;:*+SB@GB+B9A+9+ :;P:9G>@?;+@<K;i+=P+7WZZW+$+:9N+=P+E@FB>+>:9?;E@<F+@<+>B;+S9>;:+A>:@Y;A+>B;+FE9AA+9>+]6q+:;E9>@?;+>=+>B;+ <=:C9E*+9<K+>:9?;EA+>B:=LFB+>B;+J9<;W+XB9>+9<FE;*+:;E9>@?;+>=+>B;+<=:C9E*+S@EE+>B;+:9N+=P+E@FB>+D;<K+ :;E9>@?;+>=+>B;+<=:C9E+@<A@K;+>B;+FE9AAn+ ! ! ! ! ! $)-X"!+8"cH++!"#!$%&'()+^()3-+!(3).+ 4:=LJ+1;CD;:+)9C;AH+mmmmmmmmmmmmmmmmmmmmmmmmmmmmm+.9>;H++mmmmmmmmm/;:@=KH++mmmm+ 4:=LJ+pH++mmmmmmmmm+ + 7W XB9>+@A+>B;+)=:C9E+E@<;n+++ &B;+E@<;+J;:J;<K@GLE9:+>=+>B;+AL:P9G;+ 5W XB;<+K=;A+E@FB>+D;<K+>=S9:KA+>B;+<=:C9En+ + XB;<+@>+>:9?;EA+P:=C+9+E;AA+K;<A;+MP9A>;:+?;E=G@>NQ+>=+9+E;AA+K;<A;+C;K@LC+MAE=S;:+?;E=G@>NQ+ ZW XB9>+@A+>B;+AJ;;K+=P+E@FB>+@<+S9>;:n+ + ! +7WZZZ+e+MZ+"+]+CfAQf?+! ! +?+e+MZ+"+]+CfAQf7WZZZ+e+5W5T+"+]+CfA+ <+e+Gf?+! _W $+P:@;<K+>B:=SA+9+G=@<+@<>=+9+J==EW++c=L+GE=A;+N=L+;N;A+9<K+K@?;+>=S9:K+>B;+AJ=>+SB;:;+N=L+A9S+@>+ P:=C+>B;+;KF;+=P+>B;+J==EW++XB;<+N=L+:;9GB+>B;+D=>>=C*+S@EE+>B;+G=@<+D;+@<+P:=<>+=P+N=L+=:+D;B@<K+ N=Ln+ + ^;B@<K*+SB;<+N=L+9:;+=L>A@K;+>B;+S9>;:*+>B;+@C9F;+=P+>B;+G=@<+9JJ;9:A+P9:>B;:+9S9N+>B9<+>B;+9G>L9E+G=@<+ TW #@<K+>B;+@C9F;+J=A@>@=<+9<K+>B;+C9F<@P@G9>@=<+P=:+9<+=DI;G>+JE9G;K+Z+GC+=L>A@K;+>B;+P=G9E+J=@<>+=P+9+ G=<?;:F@<F+E;<A+S@>B+9+_+GC+P=G9E+E;<F>BW++.;AG:@D;+>B;+@C9F;W+ + 1/p + 1/q = 1/f ! q = (1/4 cm – 1/7 cm)-1 ! q = +9.33 cm M = -q/p ! - (+9.33 cm)/(7 cm) ! -1.33 Real, inverted, magnified + `W -LJJ=A;+9+J9<;+=P+PE@<>+FE9AA*+S@>B+9+:;P:9G>@?;+@<K;i+=P+7W`T*+@A+@CC;:A;K+@<+S9>;:*+SB@GB+B9A+9+ :;P:9G>@?;+@<K;i+=P+7WZZZW+$+:9N+=P+E@FB>+>:9?;E@<F+@<+>B;+S9>;:+A>:@Y;A+>B;+FE9AA+9>+]6q+:;E9>@?;+>=+>B;+ <=:C9E*+9<K+>:9?;EA+>B:=LFB+>B;+J9<;W+XB9>+9<FE;*+:;E9>@?;+>=+>B;+<=:C9E*+S@EE+>B;+:9N+=P+E@FB>+D;<K+ :;E9>@?;+>=+>B;+<=:C9E+@<A@K;+>B;+FE9AAn+ ! ! ni (sin! ! i) = nr(sin! ! r) ! 1.333 (sin 80º) = 1.65(sin! ! r) ! (sin! ! r) = (1.313)/1.65 ! ! r = sin-1 (0.796) = 52.7o REFRACTION, LENSES AND OPTICAL PHENOMENA EVALUATION Name: ____________________________________ Date: __________________ Period: ______ Please circle your answers for mathematical problems and you must show your work to earn any partial credit. 1) A ray of light enters the top of a glass of water at an angle of 38o with the normal. What is the angle between the refracted ray and the normal? 2) What is the index of refraction of a material in which light travels at a speed of 7.48 E 7 m/s through? 3) What is the critical angle for light traveling from benzene (n = 1.501) to ethyl alcohol (n = 1.361)? 4) If light travels from air with and angle of incidence of 14.5o into an unknown medium and refracts at an angle of 9.8o, what is the index of refraction of the unknown medium? 5) A person looks at a gem using a converging lens with a focal length of 10.25 cm. The lens forms a virtual image 26.5 cm from the lens. Determine the magnification. Is the image upright or inverted? 6) An object is placed in front of a diverging lens with a focal length of 22.75 cm. If the object is placed 15 cm in front of the lens, find the image distance and the magnification. Describe the image. 7) Michelle looks down into a pool and sees a penny on the bottom. The penny is actually 2.44 m below the surface of the water. What depth does it appear to be? 8) A convex lens has a focal length of 14 cm. Find the image distance if the object is placed at 28 cm. Is the image real or virtual? 9) A swimmer is underwater and looks at the diving board above her. The diving board appears to be 6 meters above the water. What is the actual distance of the diving board to the water? 10) What is dispersion? Give an example. 11) How will light bend (towards or away from the normal) as it travels from acetone (n = 1.36) to sapphire (n = 1.762)? 12) How do fiber optic devices transmit information? 13) Define the term laser and name three real-world application of lasers. 14) What type of image is produced by the cornea and the lens on the retina? 15) BONUS: A magnifying glass has a focal length of 15 cm. At what distance from a dime should you hold this lens to get an image with a magnification of +2? ! ! ! ANSWER KEY: REFRACTION, LENSES AND OPTICAL PHENOMENA EVALUATION Name: ____________________________________ Date: __________________ Period: ______ Please circle your answers for mathematical problems and you must show your work to earn any partial credit. 1) A ray of light enters the top of a glass of water at an angle of 38o with the normal. What is the angle between the refracted ray and the normal? ! i) = nr(sin! ! r) ! 1(sin38o) = 1.333(sin! ! r) ! ! r = sin-1 (0.616/1.333) = 27.5º ni(sin! 2) What is the index of refraction of a material in which light travels at a speed of 7.48 E 7 m/s through? n = c/v ! n = (3 E 8 m/s)/(7.48 E 7 m/s) = 4.01 3) What is the critical angle for light traveling from benzene (n = 1.501) to ethyl alcohol (n = 1.361)? sin! ! c = nr/ni ! ! c = sin-1(1.361/1.501) = 65.06o 4) If light travels from air with and angle of incidence of 14.5o into an unknown medium and refracts at an angle of 9.8o, what is the index of refraction of the unknown medium? ni(sin! ! i) = nr(sin! ! r) ! 1(sin14.5o) = nr(sin9.8o) ! nr = 1.47 5) A person looks at a gem using a converging lens with a focal length of 10.25 cm. The lens forms a virtual image 26.5 cm from the lens. Determine the magnification. Is the image upright or inverted? M = -q/p (need p first) 1/p + 1/q = 1/f ! 1/p + 1/-26.5 cm = 1/+10.25 cm ! p = [(1/+10.25 cm) – (1/-26.5 cm)]-1 = +7.39 cm M = - (-26.5 cm)/(+7.39 cm) = +3.59; Upright 6) An object is placed in front of a diverging lens with a focal length of 22.75 cm. If the object is placed 15 cm in front of the lens, find the image distance and the magnification. Describe the image. 1/p + 1/q = 1/f ! q = [(1/-22.75 cm) – (1/15 cm)]-1 = -9.04 cm M = -q/p ! -(-9.04 cm)/(15 cm) =+ 0.6 Virtual, Upright, Reduced 7) Michelle looks down into a pool and sees a penny on the bottom. The penny is actually 2.44 m below the surface of the water. What depth does it appear to be? h’/h = nr/ni ! h’ = [h(nr)]/ni ! h’ = [2.44m(1)/1.333] = 1.83 m 8) A convex lens has a focal length of 14 cm. Find the image distance if the object is placed at 28 cm. Is the image real or virtual? 1/p + 1/q = 1/f ! q = [(1/+14 cm) – (1/28 cm)]-1 = +28 cm; Real 9) A swimmer is underwater and looks at the diving board above her. The diving board appears to be 6 meters above the water. What is the actual distance of the diving board to the water? h’/h = nr/ni ! h = [h’(ni)]/nr ! h = [6 m(1)/1.333] = 4.5 m 10) What is dispersion? Give an example. Dispersion: the process of separating poly chromatic light into its component wavelengths Ex) Rainbows, prisms, etc. 11) How will light bend (towards or away from the normal) as it travels from acetone (n = 1.36) to sapphire (n = 1.762)? Towards: (FST) Fast Slow Towards; the smaller the index of refraction the faster light can travel 12) How do fiber optic devices transmit information? Light from a laser enters one end of the fiber and strikes the surface of the glass (or plastic) at an angle larger than the critical angle. This will cause total internal reflection and the light will be unable to escape until it reaches the other end of the fiber tube. 13) Define the term laser and name three real-world application of lasers. Laser: Light Amplification by Stimulated Emission of Radiation ! a device that produces an intense, nearly parallel beam of coherent light; information storage and retrieval, CD players, measurements of large distances, medical usage, scientific research (optical tweezers) 14) What type of image is produced by the cornea and the lens on the retina? Real, inverted, reduced 15) BONUS: A magnifying glass has a focal length of 15 cm. At what distance from a dime should you hold this lens to get an image with a magnification of +2? M = +2; if M = -q/p and M is +2 then q must be negative and twice as large as p; q = -2p 1/p + 1/q = 1/f ! 1/p + 1/-2p = 1/f ! 1/(2p) = 1/(15 cm) ! 2p = 15 cm ! p = 7.5 cm
© Copyright 2026 Paperzz