LECTURE 37
••
••
••
Refraction
Refraction at
at spherical
spherical surfaces
surfaces
Lenses
Lenses &
& combination
combination of
of lenses
lenses
READING
READING ASSIGNMENT
ASSIGNMENT
for
for Wednesday:
Wednesday: Section
Section 35.1-2
35.1-2
•• New
New (Last
(Last Assignment)
Assignment) will
will be
be
handed
handed out
out on
on Wednesday
Wednesday
Refraction at a single surface
& Sign convention
n1 n2 1  n2 − n1 
+ = =

s s′ f 
r 
Sign conventions
• s > 0 if object on the incident side
• s < 0 if object on the transmission
side
• s’ > 0 ifimage is on the transmission
side
• s’ < 0 ifimage on the incident side
•r > 0 if center of curvature is on the
transmission side
•r > 0 if center of curvature is on the
transmission side
Concept
Concept Test:
Test:
Which
Whichof
ofthe
thefollowing
followingstatements
statementsabout
about
the
thefigure
figureisiscorrect
correctwhen
whenthe
theindex
indexof
of
refraction
refractionnn22isisgreater
greaterthan
thannn11??
1)
1) The
Theobject
objectdistance
distanceisisgreater
greaterthan
thanthe
the
image
imagedistance.
distance.
2)
2) The
Theimage
imagedistance
distancemay
maybe
bepositive
positiveor
or
negative.
negative.
3)
3) The
Theradius
radiusof
ofcurvature
curvatureisisnegative.
negative.
4)
4) The
Themagnitude
magnitudeof
ofthe
themagnification
magnificationisis
less
lessthan
thanone.
one.
5)
5) The
Theobject
objectdistance
distanceisispositive.
positive.
Thin lenses & Sign convention
1 1 1
+ =
s s′ f
1 1
1
= ( n − 1) − 
f
 r1 r2 
Lensmaker’s eqn.
Sign conventions
• s > 0 if object on the incident side
• s < 0 if object on the transmission
side
• s’ > 0 ifimage is on the
transmission side
• s’ < 0 ifimage on the incident side
•f > 0 for a converging lens
•r > 0 for a diverging lens
Concept
Concept Test:
Test:
Ray tracing for converging lens
Case
Case I:
I: ss >> ff
Case
Case II:
II: ss << ff
Ray tracing for diverging lens
Case
Case I:
I: ss >> ff
Case
Case II:
II: ss << ff
Combination of lenses
Problem:
Problem:Two-lens
Two-lenssystem.
system.Two
Twoconverging
converginglenses
lenseswith
withfocal
focallengths
lengths
f1f1==20
cm
and
f2
=
25
cm
are
placed
80
cm
apart,
as
shown
in
20 cm and f2 = 25 cm are placed 80 cm apart, as shown inthe
thefigure.
figure.
An
object
is
placed
60
cm
in
front
of
the
first
lens.
An object is placed 60 cm in front of the first lens.
(a)
(a) Obtain
Obtainthe
thelocation
locationofofthe
thefinal
finalimage
imageby
byray
raytracing;
tracing;
(b)
Calculate
the
location
of
the
final
image
(b) Calculate the location of the final image
(c)
(c) Calculate
Calculatethe
thefinal
finalmagnification
magnification
Application: Astronomical
(refracting) telescope
Object
ii
ve
Object
velens
lens(mounted
(mountednow
nowin
in
ivory
rr
aame)
rr
oommthe
lescope
ivoryff
me)ff
thete
te
lescope
Galileo
with
ileo
GalileoGalilei
Galilei(1654-1642)
(1654-1642)
with which
which Gal
Gal
ileodiscovered
discoveredthe
the
mmoons
ffJupi
ter
..
oons oo
Jupi
ter