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Review Session 1
Dr. Flera Rizatdinova
Summary of Chapter 23
•  Index of refraction:
•  Angle of reflection equals angle of incidence
•  Plane mirror: image is virtual, upright, and the same size as the
object
•  Spherical mirror can be concave or convex
•  Focal length of the mirror:
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Summary of Chapter 23
•  Mirror equation:
•  Magnification:
•  Real image: light passes through it
•  Virtual image: light does not pass through
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Summary of Chapter 23
•  Law of refraction (Snell’s law):
•  Total internal reflection occurs when angle of incidence is
greater than critical angle:
•  A converging lens focuses incoming parallel rays
to a point
•  A diverging lens spreads incoming rays so that they appear to
come from a point
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Summary of Chapter 23
•  Power of a lens:
•  Thin lens equation:
•  Magnification:
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Multiple Choice Q1
•  An object is in front of a concave spherical mirror,
and its image is 4.0 cm behind the mirror. If the focal
length of the mirror has a magnitude of 5.0 cm,
where is the object?
•  A) 2.2 cm in front of the mirror
•  B) 2.2 cm behind the mirror
•  C) 9.0 cm in front of the mirror
•  D) 1.0 cm behind the mirror
•  Answer: A
MC Q2
•  A wrench is placed at 30 cm in front of a diverging
lens with a focal length of magnitude 10 cm. What
is the magnification of the wrench?
•  A) 0.25
•  B) -0.25
•  C) 0.67
•  D) -0.67
•  E) 4.0
•  Answer: A
Problem 1
•  A beam of light in air strikes a slab of glass (n = 1.51)
and is partially reflected and partially refracted.
Determine the angle of incidence if the angle of
reflection is twice the angle of refraction.
•  Answer: 81.9°
Problem 2
•  An object is placed 9.5 cm in front of a convex lens
with a focal length of magnitude 24 cm.
•  (a) Where is the image formed and how far is it from
the lens?
•  (b) What is the magnification produced by the
lens?
•  Answer: (a) 16 cm in front of the lens (b) 1.7
Problem 3
•  A bright object and a viewing screen are separated
by a distance of 86.0 cm. At what location(s)
between the object and the screen should a lens of
focal length 16.0 cm be placed in order to produce
a sharp image on the screen?
•  Answer: do=64.7cm and do =21.3 cm
Summary of Chapter 24
•  Wavelength of light in a medium with index of refraction n:
•  In the double-slit experiment, constructive interference occurs
when
•  and destructive interference when
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Summary of Chapter 24
•  Light bends around obstacles and openings in its path, yielding
diffraction patterns
•  Light passing through a narrow slit will produce a central
bright maximum of width:
•  The intensity of plane polarized light is reduced after it passes
through another polarizer:
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MC Q3
•  Blue light of wavelength λpasses through a single slit of width
d and forms a diffraction pattern on a screen. If we replace
the blue light by red light of wavelength 2λ, we can retain
the original diffraction pattern if we change the slit width
•  (a) to d/4.
•  (b) to d/2.
•  (c) not at all.
•  (d) to 2d.
•  (e) to 4d.
•  Answer: D
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Problem 4
•  Light of wavelength 470 nm in air shines on two slits 6.00 × 10–2
mm apart. The slits are immersed in water, as is a viewing screen
40.0 cm away. How far apart are the fringes on the screen?
•  Answer: 2.4 ×10-3 m
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Problem 5
•  When yellow sodium light, λ= 589 nm, falls on a
diffraction grating, its first-order peak on a screen
72.0 cm away falls 3.32 cm from the central peak.
Another source produces a line 3.71 cm from the
central peak. What is its wavelength? How many
slits/cm are on the grating?
•  Answer: 658 nm; 782 lines/cm
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Problem 6
•  Two polarizers are oriented at 48° to each other and
plane-polarized light is incident on them. If only 35%
of the light gets through both of them, what was the
initial polarization direction of the incident light?
I1 = I 0 cos2 θ1; I 2 = I1 cos2 θ 2 = I 0 cos2 θ1 cos2 θ 2 = 0.35I 0 →
# 0.35 &
# 0.35 &
( = cos−1 %
( = 28°
θ1 = cos−1 %%
(
% cos 48° (
cos
θ
$
$
'
2'
Problem 7
•  Four polarizers are placed in succession with their axes vertical,
at 30.0° to the vertical, at 60.0° to the vertical, and at 90.0° to
the vertical. (a) Calculate what fraction of the incident
unpolarized light is transmitted by the four polarizers. (b) Can
the transmitted light be decreased by removing one of the
polarizers? If so, which one? (c) Can the transmitted light
intensity be extinguished by removing polarizers? If so, which
one(s)?
I1 = 1 I 0 ; I 2 = I1 cos2 θ 2 = 1 I 0 cos2 θ 2 ;
2
2
I 3 = I 2 cos2 θ3 = 1 I 0 cos2 θ 2 cos2 θ3;
2
I 4 = I 3 cos2 θ 4 = 1 I 0 cos2 θ 2 cos2 θ3 cos2 θ 4 =
2
1 I cos 2 30.0°cos 2 30.0°cos 2 30.0° = 0.211I
0
2 0
Cont’d
• 
If the second polarizer is removed, then the angle between polarizers
1 and 3 is now
I1 = 1 I 0 ; I 3 = I1 cos2 θ3 = 1 I 0 cos2 θ3;
2
2
I 4 = I 3 cos2 θ 4 = 1 I 0 cos2 θ3 cos2 θ 4 = 1 I 0 cos2 60.0°cos2 30.0° = 0.0938 I 0
2
2
The same value would result by removing the third polarizer, because
then the angle between polarizers 2 and 4 would be The intensity can
be decreased by removing either the second or third polarizer.
If both the second and third polarizers are removed, then there are still
two polarizers with their axes perpendicular, so no light will be
transmitted.
Summary of Chapter 25
•  Simple magnifier: object at focal point
•  Angular modification:
•  Astronomical telescope: objective and eyepiece; object
infinitely far away
•  Telescope magnification:
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Summary of Chapter 25
•  Compound microscope magnification:
! N $ ! l − fe $
M = # &#
&
" fe % " d o %
•  Resolution of optical devices is limited by diffraction
1.22 λ
θ=
D
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Problem 8
•  A nearsighted person has a far point of 18 cm.
What power contact lenses will allow this person to
comfortably see distant objects clearly?
•  A) +5.6 diopters
•  B) -5.6 diopters
•  C) +0.056 diopters
•  D) -0.056 diopters
•  Answer: B
Problem 9
•  The objective lens of a microscope has a focal length
of 2.4 mm and the eyepiece has an angular
magnification of 15. The object is positioned 0.060
mm beyond the focal point of the objective. The
focal point of the eyepiece is positioned at the real
image formed by the objective. The near point of the
microscope user is at 25 cm. What is the magnitude
of the overall magnification of the microscope?
•  Answer: 600