PHYS 252 FINAL EXAM 4/30/08 Dr. Holmes NAME
DO ALL 15 PROBLEMS. THE WORTH OF EACH PROBLEM IS MARKED BESIDE THE PROBLEM. SHOW YOUR WORK FOR PARTIAL CREDIT.
1) A ray of light in water (assume n = 1.33 for water) hits a water/air (assume n = 1.00 for air) interface at an angle of 66 degrees with respect to the SURFACE of the interface.
a)What is the angle of reflection measured from the SURFACE?
66 degrees.
b)What is the angle the transmitted ray in the air makes with the NORMAL (if totally reflected, answer TIR)?
32.75 degrees.
c) Can rays of light in the water be totally reflected from the water/air interface?
Yes.
d) Can rays of light in the air be totally reflected from the air/water interface?
No.
2) A magnifying glass has a focal length of 20 mm.
a) What is the magnification of this lens when used properly?
13.5 X
b) What should the image distance be if it is used “properly” ?
-25 cm
3) Draw a diagram showing the object, lens, image, eye, and focal points for the lens.
3) a) Design a lens with the focal length of the above magnifying glass (specify the index of refraction, n, and the radii of the front and back surfaces R1 & R2):
n =
R1 =
R2 = (many answers are possible)
b) DRAW A PICTURE of this lens showing the relative curvatures:
4) Laser light of wavelength 6332 nm is directed through a double slit with a distance of 0.15 mm between slits and each slit having a width of 0.030 mm. The screen is 8 meters away.
a) How far apart are adjacent bright spots on the screen?
3.4 cm.
b) If the distance between slits is increased, will the distance between adjacent bright spots increase, decrease, or remain the same?
decrease.
c) If the width of each of the two slits is increased, will the distance between adjacent bright spots increase, decrease, or remain the same?
remain the same.
d) If the wavelength of the light is decreased, will the distance between adjacent bright spots increase, decrease, or remain the same?
decrease.
For problems 5 & 6: A camera with a 50 mm focal length lens takes a picture of a newspaper with print that is 5 mm in size and the paper is 100 meters away. The person uses an f-stop of 4 (meaning the diameter of the opening of the lens is 50mm / 4 = 12.5 mm) and time exposure of 1/120 second. The film is 24 mm x 36 mm.
5) a) What is the object distance?
100 m.
b) How far should the lens be from the film? (If the distance is close to the focal length, be sure to indicate whether the distance is a little more than or a little less than the focal length)
50.03 mm.
c) What is the size of the print on the film?
2.5 micrometers.
6) Use the information on the camera above.
a) What angle does the print size make with the lens at the 100 meter distance?
2.86 x 10-3 o = 5 x 10-5 radians
b) What is the smallest angle this camera can resolve using the f-stop of 4?
3.08 x 10-3 o = 5.37 x 10-5 radians
c) If the film is enlarged, will you be able to resolve the letters well enough to be able to read the paper from the enlarged picture? (answer defintiely, just barely or not quite, or definitely not)
definitely not.
7) Consider a person with an average skin temperture of 94oF and a surface area of 1.2 m2.
a) What is the average temperature of the person’s body:
in oC: 34 degrees C
in Kelvin: 307 K.
b) At this temperature, what is the wavelength at which the intensity of radiation peaks?
9.43 m m = 9.43 x 10-6 m.
c) What color (if visible) or type (such as IR, UV, etc) of light is this?
IR.
d) What is the total amount of radiation the person’s body emits (in Watts):
609 Watts.
f) If the air temperature is -40oF, how much radiation would the person’s body absorb?
200 Watts.
8 a) If the cut-off wavelength for light to eject photo-electrons from a particular metal is 350 nm, what is the work function for this metal?
3.55 eV = 5.68 x 10-19 Joules.
b) What kind of light is this (if visible, what color) ?
UV.
c) Will light of wavelength 382 nm be able to eject electrons from the metal?
No.
9) a) What is the ground state energy of the hydrogen atom?
-13.6 eV = -2.18 x 10-19 Joules.
b) How much energy is emitted when the electron falls from the n=4 state to the n=1 state in the hydrogen atom?
12.75 eV = 2.04 x 10-18 J.
c) What type of photon is this (e.g., ultraviolet, infrared, etc. (if visible, specify the color):
UV.
10) Two explosions (call them # and $) are seen by observer A: the $ explosion happens 2,300 meters to the right of the #, and the $ explosion happens 4 microseconds after the # explosion. Observer B is moving with a speed of .777c to the left with respect to the A observer.
a) What does observer B measure for the distance between the two explosions?
5,135 m.
b) Did the $ explosion happen to the right or left of explosion # according to observer B?
right.
c) What does observer B measure for the time difference between the two explosions?
15.8 m sec = 15.8 x 10-6
seconds.
d) Which explosion happened first (# or $) as determined by observer B?
# .
11) A spaceship moving at a speed of 0.58c toward the earth (as measured by both the earth and the spaceship) fires a missile going toward the earth at a speed of 0.66c relative to the spaceship.
a) What speed would an earth observer measure for the missile?
0.897 c.
b) Is the missile going toward the earth or away from the earth?
Toward.
c) If the missile were fired at a speed of 0.66c away from the earth (as measured by the spaceship) instead of toward it (with the spaceship still going 0.58c toward the earth), what speed would the earth observer measure for the missile?
0.13 c.
d) Is the missile now going toward the earth or away from the earth?
Away from.
e) If the missile were replaced by a light pulse directed away from the earth, what speed would the earth meaasure for the speed of the light pulse?
c.
12) A photon has energy 6.54 keV (6,540 eV).
a) What is the wavelength of light that has photons of this energy?
0.190 nm = 1.90 x 10-10 m.
b) What type of light is this (IR, UV, radio, etc.; if visible, what color is it)?
x-ray.
c) What is the mass of this photon?
1.16 x 10-32 kg.
d) What is the rest mass of this photon?
zero.
e) What is the momentum of this photon?
3.49 x 10-24 kg*m/sec.
Mass of Hydrogen atom (proton + electron) = 1.00782 amu;
mass of neutron = 1.008665 amu; mass of electron = .00055 amu;
rest mass energy of an amu = 931.5 MeV.
If you do not know the symbol of an element but only know its atomic number and
mass number, then use X as the symbol of the element.
13) a) What is the total nuclear binding energy for iron-16 (26Fe56) which has an atomic mass of 55.9349 amu)?
492.2 MeV.
b) What is the binding energy per nucleon?
8.79 MeV/amu.
c) Is this binding energy per nucleon greater, the same, or less than that for carbon-14 (6C12 has an atomic mass of 12.0000 amu by definition)?
greater.
14) Fill in the missing particle(s), given that there are no stable isotopes of Radon (Rn); there is 1 stable isotope of Rh at 103.
86Rn222 goes to 84X218 + alpha + energy
45Rh100 goes to +
44X100 + +1b 0 + neutrino
45Rh105 goes to + 46X105
+ -1b 0
+ antineutrino
15) a) What is the activity of a sample of 1 gram of 45Rh105 given that its half life is 36 hours?
In Bq: 3.06 x 1016 in Curies: 826,000
b) What will be the activity of the 1 gram sample of Rh105 (in Bq) after 1 month (30 days)?
2.92 x 1010 Bq.