Practice Problems – Part 3
TF: Widagdo Setiawan, widagdos@gmail.com
www.ps3section.com
There are a lot more (free) solved problems if you google: “scribd 1000 solved problems in classical
physics“
1. Shown below is a ray diagram for an object and a diverging lens. Which of the rays drawn is NOT a
principal ray?
2. A small object is placed 5 cm behind a magnifying glass. The image one sees through the lens appear
3 times larger than the actual object. What is the focal length of the magnifying glass?
3. Assuming that the dots are at the focal length, which of the following paths is drawn incorrectly?
4. Microscope
The figure below (not drawn to scale) shows a schematic of how a compound microscope works.
There are two lenses: an objective lens and an eyepiece lens. Light from the sample first passes
through the objective lens, which produces a first image 𝐼1 that needs to be located just inside the
focal point of the eyepiece. That first image then becomes the object for the eyepiece lens, which
produces a second image that is seen by the eye. For this problem we will assume that the focal
length of the objective lens is 𝑓0 = 1.0 cm, the focal length of the eyepiece is 𝑓𝑒 = 3.0 cm, and the
object is a distance 𝑑0 = 1.2 cm from the objective lens.
a. Find the distance 𝐿 between the two lenses so that the image formed by the objective is
1 mm inside the focal point of the eyepiece.
b. Make a ray diagram that shows the location of the image formed by the eyepiece lens.
5. Standard two slits interference problem
Derive the equation that describe the locations of the bright bands and dark bands in a two slits
system where the slit separation is 𝐷.
6. Two slits interference with a piece of glass on one of the slit.
Start with a typical two slits interference setup, one slit at the top and another one at the bottom.
But on the top slit, we put a piece of glass with index of refraction 𝑛 and thickness 𝑡. We then put a
screen at some location far away from the slits at distance 𝐿. Where are the locations of the bright
fringes? Assume that the wavelength of light is 𝜆. If you increase the thickness of the glass, will the
fringes move up or down? You can assume that 𝜃 is small.
7. The picture below shows the intensity of light vs. position on a screen for a double-slit experiment.
At the second maximum on either side of the central bright spot, _______
a.
b.
c.
d.
Light from each slit travels the same distance
Light from one slit travels twice as far as the light from the other slit
Light from one slit travels one wavelength of light farther than light from other slit
Light from one slit travels two wavelengths of light farther than light from other slit
8. Radio Broadcast Pattern
An AM radio station operating at a frequency of 1500 kHz has two identical vertical antennas
spaced 400 m apart, broadcasting in phase. Naturally, the radio station is concerned about regions
where the signal has low intensity. At what angular locations (measured relative to a vertical axis)
will listeners at distance much greater than 400 m experience a minimum in intensity?
9. Interference by Reflection
Monochromatic light of wavelength 𝜆 is normally incident on the surface of a CD, as shown below.
The CD surface consists of alternating rows of reflective and non-reflective parts, with a spacing of
𝑑 = 1.6 𝜇𝑚. In addition to the directly reflected beam at 𝜃 = 0, three more bright spots are seen on
either side.
a. Explain why these additional bright spots appear, and derive an equation which gives the
angles at which the bright spots will be found.
b. Based on the information given and the equation you derived in part a, what range of values
is possible for the wavelength 𝜆.
10. Thin film interference
White light reflect at normal incidence on a very thin soap film with air on either side of it. Describes
what happens with the reflected ray as you increase the thickness of the soap film.
11. True false question
A laser beam with wavelength 𝜆 shines on a soap bubble with index of refraction 𝑛. The thickness of
the bubble is exactly 𝑡 =
𝜆
.
4𝑛
Which of the following(s) are true?
a. There is constructive interference on the reflection.
b. The soap bubble looks bright on reflection
c. There is no transmitted laser beam.
12. Stationary electrons are accelerated by two plates with potential difference 1 𝑉. The electrons then
go to a double slit, separated by 1 𝜇𝑚. The electrons are detected on a detector 1 meter away from
the double slit. What is the spacing between two peaks on the detector?
13. Double slit with lens. The double slit formula assumes that the screen is located very far away. In
real experiment however, putting a screen far away is not practical. To solve this, we can put a lens
in between the screen and the slits. Assuming that the screen is at a distance 𝐿 from the slits, the
spacing between the slits is 𝑑 and the focal length of the lens is 𝑓, how far away from the slits 𝑥
should I put the lens?
14. The images of two point sources of light are recorded on photographic paper using a thin slit. The
point sources are separated by 1 cm and emit light with wavelength 500 nm. The point sources are
10 m away from the slit, and the photographic paper is 100 cm behind the slit. How wide does the
slit have to be in order to generate distinct images of the two point sources.
15. When light of wavelength 540 nm passes through a single slit of unknown width, the diffraction
pattern displays a second maximum where the first minimum of light of an unknown wavelength
had been observed to fall. What is the unknown wavelength?
16. Which of the following objective lenses would provide the best resolving power?
a. Lens diameter = 8 mm; focal length = 2 mm
b. Lens diameter = 12 mm; focal length = 2 mm
c. Lens diameter = 14 mm; focal length = 4 mm
d. Lens diameter = 18 mm; focal length = 4 mm
17. Betelgeuse is an unusually large star, with radius of 5 × 1011 m. (That’s 650 times larger than the
Sun). It is about 400 light years away from us. What is the minimum diameter of the telescope that
can see Betelgeuse as a disc and not as a point? Assume that the wavelength of the light from
Betelgeuse is 600 nm.
18. Concept questions:
a. What are the differences between bubble interference and oil spill interference?
b. In a double slit experiment, what will you see if you put the screen really really close to the slits?
Will you see any interference?
c. You perform a double slit experiment, and you measure the distance between two peaks as Δ𝑥.
You then pour a liquid with index of refraction 𝑛 on your setup. Will the distance between the
peaks on the interference patter change? If it does, by how much? Explain.
d. True/False. The Hubble Space Telescope (HST) is diffraction limited. Its angular resolution is
therefore better at short wavelengths (e.g. blue light) than at longer wavelength (e.g. red light).
e. True/False. Red laser light has a smaller wavelength in water than in air
19. Where should you put color filters inside a modern microscope?
a. Between the objective and the specimen
b. Between the objective and the tube lens
c. Between the tube lens and the eyepiece
d. Between the eyepiece and the eye
20. Two polarizing sheets have their polarizing directions parallel. Determine the angle by which either
sheet must be turned so that the intensity falls to half of its value.
21. Dolphins
Dolphins use echolocation to learn about their underwater surroundings, where visible light is much
less effective. They emit high frequency “clicks” and detect the echoes that echoes that return after
bouncing off nearby objects. For this problem we will assume that the clicks emitted by the dolphin
have a frequency of 100 𝑘ℎ𝑧 and a wavelength of 15 mm.
a. A dolphin detects the presence of a submarine. The dolphin sends out one click and detects the
echo 40 𝑚𝑠 later. How far away is the submarine?
b. Assume that a dolphin can detect a frequency shift of 1 part in 100. If a fish is swimming directly
away from the dolphin, what is the slowest speed the fish could have that would be detectable
to a stationary dolphin?
c. A dolphin swims towards a boat with speed 𝑣 relative to the water. At the same time, the boat
is moving towards the dolphin with speed 𝑢 relative to the water. If the dolphin emits a click
with frequency 𝑓0, what is the frequency of the echo 𝑓𝑒ℎ𝑐𝑜 received by the dolphin? Assume that
the speed of sound in water is 𝑤.
22. Air in a pipe that is closed at both ends supports a standing sound wave with fundamental frequency
of 300 hz. Ig a small hole is opened in the pipe exactly halfway along its length, what will be the two
lowest allowed frequencies for the standing waves in the pipe?
23. A train is approaching you at very high speed as you stand next to the tracks. Just as an observer on
the train passes you, you both begin to play the same Beethoven symphony.
a. According to you, whose music finishes first?
b. According to the observer on the train, whose music finishes first?
c. Whose music really finishes first? Neglect special relativity effect.
d. Which one observes a larger difference in finishing time? You or the observer on the
train, or maybe both observed the same time difference?
24. A source emits a wave with frequency 𝑓. If you want to observe a frequency 2𝑓, two ways of
accomplishing this are: 1. Have the source bet at rest with you moving towards it, or 2. Have you be
at rest with the source moving towards you. Which of these strategies requires the smaller speed?
a. The first one
b. The second one
c. They require the same speed
1
25. A source emits a wave with frequency 𝑓. If you want to observe a frequency 2 𝑓, two ways of
accomplishing this are: 1. Have the source bet at rest with you moving away from it, or 2. Have you
be at rest with the source moving away from you. Which of these strategies requires the smaller
speed?
a. The first one
b. The second one
c. They require the same speed
26. What are the differences between string standing wave and half closed pipe standing wave?
(Fundamental wavelength, fundamental frequency, general frequencies (harmonics), longitudinal /
transverse, displacement)
27.