April 28, 2000 Physics 208

**Exam 3**

Print your name and section clearly on all five pages. (If you do not
know your section number, write your TA’s name.) Show all work in the space
immediately below each problem. Your final answer must be placed in the
box provided. Problems will be graded on reasoning and intermediate steps
as well as on the final answer. Be sure to include units wherever necessary,
and the direction of vectors. Each problem is worth 25 points. In doing
the problems, try to be neat. Check your answers to see that they have
the correct dimensions (units) and are the right order of magnitudes. You
are allowed one 8½ x 11" sheet of notes and no other references.
The exam lasts exactly 50 minutes.

*(Do not write below)*

SCORE:

Problem 1: __________

Problem 2: __________

Problem 3: __________

Problem 4: __________

**TOTAL: ___________**

1. A thin converging lens with a focal length of 10 cm is placed directly next to a thin diverging lens with a focal length of -20 cm. An object of height 10 cm is placed 25 cm in front of the lenses.

a. Where is the image located? *(10 pts.)*

b. What is the height of the image? *(10 pts.)*

c. Is the image real or virtual, upright or inverted? *(5 pts.)*

2. Two slits a distance 1 mm apart are illuminated with coherent, monochromatic light and produce an interference pattern on a screen 10 m away. The distance between successive bright bands on the screen is 5 mm.

a. What is the wavelength of the light? *(9 pts.)*

3. An astronaut, initially 20 years old, makes a journey to a point
in the galaxy that is 10 light-years from the earth (as measured by a stationary
observer on the earth) in a rocket ship that travels at a speed *v*
= 0.8*c* relative to the earth.

a. If the astronaut left the earth in the year 2080 and remained at
her destination for one year, and then returned to the earth at the same
speed, what year would it be when she returned? *(7 pts.)*

b. How old would she be when she returned? *(6 pts.)*

c. How many light years would the rocket ship’s odometer have registered?
*(6 pts.)*

d. What minimum fraction of the rocket ship’s mass would have to be
annihilated to achieve a velocity of 0.8*c*? *(6 pts.)*

4. A hydrogen atom decays from its first excited state to its ground state.

a. What is the energy of the photon emitted? *(5 pts.)*

b. What is the wavelength of the photon emitted? *(5 pts.)*

c. If this photon is incident on a metal with a work function of 3 eV,
what is the maximum kinetic energy (in eV) of the electron that is ejected
from the metal? *(5 pts.)*

d. If the photon collides head-on with a free electron (*m*_{e}
= 9.1 x 10^{-31} kg) initially at rest and the photon recoils backwards,
how much energy (in eV) is imparted to the electron? *(5 pts.)*

e. What is the value of *gamma* – 1 for the electron in part d
above? *(5 pts.)*