Physics 204 Final (B)

Lecturer: Dr. Min Xu

Dec 22, 2003
LAST NAME: ___________________________________________________________________________________________________ FIRST NAME: __________________________________________________________________________________________________ SS# (last 4 digits): _____________________________________________________________________________________________

General Instruction

You have 2 hour 15 minutes to answer 9 questions on this exam. Work each problem only on the sheet provided for this problem, using the back if necessary. Please write the name and recitation section on each sheet at the top of the page.

You must indicate the reasoning and show all the steps.

If you are unable to obtain the answer to part of a problem and you need the answer to solve the subsequent parts, use an appropriate symbol for the answer to the previous part and solve in terms of that symbol.

Some useful constants and formulas are given here:

me = 9.1 × 10- 31kg -7 m0 = 4p× 10 W b/A .m e0 = 8.85 × 10 -12C2/N .m2 -19 e = 1.60 × 10 C k = --1-- = 9.0 × 109N .m2/C2 4pe0 B = m0I/(2pr) F = qvB sin(h) F = ILB sin(h) e = -N DP/Dt sin hmin = c/W sin hmin = 1.22c/D h = 6.62 × 10 -34J .s c = h/p vAB = --vAC-+-vCB---- 1 + vACvCB/c2 c = 3.0 × 108m/s DpyDy > h/(2p) ' h 1/c - 1/c = ---(1- cosh) mc

1. (5 points) Explain the fact that you see yourself upside down when you look at the front side of a shiny teaspoon held at arm’s length. Draw a ray diagram to support your reasoning.

2. (10 points) The eye of human being can not resolve the headlights of a car far away. Why? Estimate the distance at which one can hope to distinguish the headlights of a car. The pupil of your eye has a diameter of 2mm. The visible light has a wavelength of about 500nm.

3. (5 points) A cruiser approaches an alien spacecraft in a speed close to that of light c and fires an ion gun at the alien spacecraft. The ion leaves the cruiser at a speed of close to c observed by the fighter aboard the cruiser. However, the alien finds that the ion only moves away from the cruiser very slowly. Explain.

4. (5 points) The wave-particle duality is now accepted as an essential part of nature. Please give two experiments where the electron demonstrates its wave and particle characteristics respectively.

5. (20 points) A piece of glass, of index of refraction n = 1.5, has one surface polished into a sphere of radius 5cm, as shown. The normal to a sphere is always along a radius. Rays of light strike the glass from the left, as shown.


(a) (10 points) Find the incident and refraction angles of the ray at the height of h = 3cm. Mark them clearly on the figure.
(b) (10 points) Find the image of upright object in front of the glass at a distance of 1cm graphically by using the principle rays viewed inside the glass. Mark the rays and the image clearly. Is the image real or virtual? How big is the magnification of the object by measuring your drawing?

PIC

6. (10 points) In an experiment, a glass plate (nglass = 1.5) lies under a film of soap (nsoap = 1.33). Visible light is incident almost normal to the plate. Maxima of reflected light are observed at 406nm and 609nm. What is the thinnest that the film can be?

7. (15 points) Electrons are moving with a velocity 5 × 106m/s. These electrons are used to perform the Young’s double slit experiment where the separation between the two slits is d = 0.1mm and the detector is placed at a distance of L = 5m behind the slits.


(a) (5 points) What is the De Broglie wavelength of these electrons?
(b) (5 points) How far is the first dark fringe away from the central bright fringe?
(c) (5 points) Suppose the beam from ONE slit is retarded by one-half De Broglie wavelength by the introduction of some electromagnetic field in that region, what will happen to the fringe patterns? Explain.

8. (15 points) A person runs 100m in 10s in a train along a straight line in the same direction as the train moves. The train moves at a velocity 0.8c relative to the ground. c is the speed of light.


(a) (5 points) What is the time taken by the runner observed by the person on the ground?
(b) (5 points) What is the speed of the runner observed by the person on the ground?
(c) (5 points) How far does the runner run observed by the person on the ground?

9. (15 points) In the Bohr’s Hydrogen atom model, the energy levels are given by: En = (-13.6ev)/n2 where n = 1, 2, 3,....


(a) (5 points) An electron drops from the excited state (n = 2) to the ground state (n = 1) and emits a photon. What is the wavelength of the emitted photon?
(b) (5 points) Find the radius a of the orbit of the ground state using the fact E1 = -1 2ke2/a.
(c) (5 points) Consider an electron confined in a box of size equal to a (obtained previously). What is the uncertainty of the momentum and energy of the electron? How does the uncertainty of the energy compare to the energy of the ground state -E1 = 13.6ev of the Hydrogen atom?