**1. (40 points)** **A thin film of cryolite (n = 1.35) of thickness d is applied to thick layer of oil (n = 1.25). See the diagram below. Assume the incident light traveling in water (n = 1.33), has wavelength 575 nm in a vaccum and is normal to the water-cryolite interface.**

- (20 points)What minimum non-zero thickness
*d*will create bright__reflected__light? - (20 points)What minimum non-zero thickness
*d*will create bright__transmitted__light?

Solutions: note that you must use n = 1.35 for the layer.(a) 2nd = (m + 1/2)*(575 nm ) with m = 0 so that d = 106 nm. (b) 2nd = m *575 nm so that d = 213 nm when m = 1. |

**2. (40 points) A screen is placed 0.60 m from a single slit. The illumination light is of wavelength 690 nm.
(a) (20 points) If the distance from the 2nd to the 4th minimum in the diffraction pattern is 2.0 mm = 0.0020 m, then what is **

__principle maximum centered about the axis__.

Solutions: (a) y4 - y2 = 2(690 nm)*L/ a = 0.002 m, so
that a = 2(690 nm)*L/(y4 - y2) = 4.14x10^{-4 }m (b) See problems 3 and 7 of Quiz 10. |

3. EC (9 points)Two small rockets A and B fly toward each other at speed 0.80 c relative to the earth.

(a) (3) What is the speed of A relative to B?

(b) (3) What is the speed of B relative to A?

(c) (3) Suppose the length of the rocket A relative to the A reference frame is 300 m. (This is called the proper length.) What is the length of rocket A relative to the __B-reference frame__?

Solutions: (a) (0.8c + 0.8c)/(1 + 0.8*0.8) = 0.976 c (b) 0.976 c from symmetry. (c) L = 300*(1 - 0.976)2)1/2 = 65.9 m |