Question

1.)A manganese vapor laser beam is reflected from the surface of a CD onto a wall. The brightest spot is the reflected beam at an angle equal to the angle of incidence. However, fringes are also observed. If the wall is 1.6 m from the CD, and the first bright fringe is 0.583 m from the central maximum, what is the spacing (in m) of grooves on the CD? (Assume a manganese vapor laser has a wavelength of 534 nm. Also assume that the main reflected beam incident on the wall is exactly perpendicular to the wall.)

2) An oil slick on water is 82.3 nm thick and illuminated by white light incident perpendicular to its surface. What color does the oil appear (what is the most constructively reflected wavelength, in nanometers), given its index of refraction is 1.43? (Assume the index of refraction of water is 1.33.)

Answer 1

1)

= arctan ( 0.583 / 1.6) = 20.02 degree

so,

m = d sin

d = m / sin

d = 1 * 534e-9 / sin 20.02

d = 1.56e-6 m

________________

2)

2nt = ( m + 1/2)

where m = 0,1,2....so on

2 * 1.43 * 82.3e-9 = ( m + 1/2)

first put m = 0

= 471 nm

for m = 1

= 157 nm ( this is out of visible range)

so,

= 471 nm