23.6
23.6
Exercise
32. A convex lens of focal length 15.0 cm is used as a magnifying
glass. At what distance from a postage stamp should you hold this
lens to get a magnification of +2.00?
+draw ray diagram
36. An object’s distance from a converging lens is ten times the
focal length. How far is the image from the focal point? Express the
answer as a fraction of the focal length.
+draw ray diagram
Combinations of thin lenses
object
image,
image,
lens 2
lens 1 = object,
lens 2
Exercise
41. Two converging lenses, each of focal length 15.0 cm, are placed
40.0 cm apart, and an object is placed 30.0 cm in front of the first.
Where is the final image formed, and what is the magnification of
the system?
23.7 lens & mirror aberrations (read)
Where is the
observer?
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College Physics W04 Prof. Kinoshita
Chapter 24 Wave optics
conditions for interference
Young's double slit experiment
change of phase due to reflection
interference in thin films
24.2 Young's double-slit interference
(read description)
diffraction
single-slit diffraction
diffraction grating
polarization of light waves
Schematic w ordinary light source
____________________________________________________________________________________________________________________________________
24.1 conditions for interference (read)
EM waves - high frequencies -> to observe interference, need
1. The sources must be coherent – that is, they must maintain a constant phase with
respect to each other.
2. The waves must have identical wavelengths.
Coherence of visible light:
• ordinary sources: cohereint (continuous wave) over <10–8s ≡ incoherent
•2 "
" have random, changing relative phase -> NOT coherent
Achieve coherence by
• ordinary source, shone thru single slit
-> multi-slit mask
• laser
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double slit =
coherent
slit sources
"single source"
interference fringes (dark)
path difference <-> phase difference
wavefronts
constructive interference
where crests intersect
destructive interference
where crest intersects trough
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24.2
Quantitatively,
P "far" ~∞
-> approx parallel, angle θ to normal
-> path diff. δ~d sin θ
for constructive interference:
δ = dsinθ =mλ (eq. 24.2)
Location on screen:
y = Ltanθ ~ Lsinθ (eq. 24.4)
0,±1,±2, … order #
(zeroth, first, … order)
for destructive interference:
for small angles
bright fringes:
δ = dsinθ =(m+1/2)λ (eq. 24.3)
24.2
Exercise
3. A pair of narrow, parallel slits separated by 0.250 mm are
illuminated by the green component from a mercury vapor lamp
(wavenength = 546.1 nm). The interference pattern is observed on a
screen 1.20 m from the plane of the parallel slits. Calculate the
distance (a) from the central maximum to the first bright region on
either side of the central maximum and (b) between the first and
second dark bands in the interference pattern.
ybright = λ L/d • m (eq. 24.5)
dark fringes:
0,±1,±2, …
ydark = λ L/d • (m+1/2) (eq. 24.6)
(demo)
0,±1,±2, …
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College Physics W04 Prof. Kinoshita
24.3 Change of phase due to reflection
(read about Lloyd's mirror, p. 752)
Bottom line:
lower->higher n
analogy: fixed end
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higher->lower n
analogy: free end
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