Question

A laser beam enters a 19.0 cm thick glass window at an angle of 39.0° from the normal. The index of refraction of the glass is 1.50. At what angle from the normal does the beam travel through the glass? Tries 0/20 How long does it take the beam to pass through the plate?

Answer 1

Solution :

Given :

Thickness of glass window (d) = 19 cm = 0.19 m

Angle of incidence (i) = 39.0°

The index of refraction of the glass (ng) = 1.50

Part (a) : At what angle from the normal does the beam travel through the glass :

Now: Using a snell's law : nair sin i = ng sin r

(1) sin 39o = (1.5) sin r

r = sin-1 [(0.629) / (1.5)] = 24.8o

Part (b) : How long does it take the beam to pass through the plate?

Distance travelled by the beam in glass is given as : x = d / cos r = (0.19 m) / cos 24.8o = 0.209 m

And, Speed of the beam in glass (vg) = c / ng = (3 x 108 m/s) / (1.5) = 2 x 108 m/s

Time taken by the beam to pass through plate will be given as :

t = d / v = (0.209 m) / (2 x 108 m/s)

t = 1.05 x 10-9 sec

t = 1.05 ns