A laser beam strikes one end of a slab of material of length

A laser beam strikes one end of a slab of material of length L = 42.0 cm and thickness t=3.10 mm. Itenters the material at the center striking it at an angle of incidence of 50.0 degrees. The index of refraction of the slab is n = 1.48. How many internal reflections the light makes from the top and bottom of the slab before exiting at the other end.

Solution

As the beam enters the slab

n1*sin A1 = n2*sin A2

1*sin 50 = 1.48*sin A2

A2 = arcsin(sin 50/1.48) = 31.2 deg

the beam then stirkes at the top of slab at x1

x1 = 1.55*10^-3/tan 31.2 = 2.56*10^-3 m (from the left end)

After that the beam strike at slab each time it has traveled a distance of 2x1

Since the slab is 42 cm long, total distance to travel after first reflection = 42 cm - x1

(42 cm - x1)/2x1 = (42*10^-2 - 2.56*10^-3)/(2*2.56*10^-3) = 81.53 reflections

Since the number of reflection will be integer, So total number of reflections will be 82.