Question

1) A laser beam enters a 12.0 cm thick glass window at an angle of 66.0° from the normal. The index of refraction of the glass is 1.42. At what angle from the normal does the beam travel through the glass?

I know this one is 40.04 degrees.

I am stuck on this one:

2) How long does it take the beam to pass through the plate?

Answer 1

let x = thickness of glass = 12 cm = 0.12 m
Oi = angle of incidence = 66o
ni = index of refraction of air = 1.0003
nr = index of refraction of glass = 1.42
c = speed of light in vacuum = 3 x 10^8 m/s
v = speed of beam in glass
t = time for the beam to pass through the glass
Or = angle of refraction = ?

a. using snell's law: ni(sinOi) = nr(sinOr)
Or = arcsin (ni(sinOi)/nr)
= arcsin(1.0003(sin66o)/1.42)
= 40.055o

b. ):
d = x/cosOr
= (0.12 m)/(cos 40.055o)
= 0.156 m
find the speed of the beam in the glass:
v = c/nr
= (3 x 10^8 m/s)/1.42
= 2.112 x 10^8 m/s
Find the time for the beam to pass through the glass:
t = d/v
= (0.156 m)/(2.112 x 10^8 m/s)
= 7.393 x 10^-10s