Question

In winter a lake has a 0.35 m thick ice layer over 1.50 mof water. A light beam from above strikes a spot on the ice, making a 29 ∘ angle with the normal.

How far horizontally from that spot does the light ray strike the lake bottom?

Answer 1

refractive index of ice , n1 = 1.31

refractive index of water , n2 = 1.33

for ray from air to ice:

Applying snell's law to find refractive angle

ni sini = nr sinr

1 * sin29 = 1.31 * sin@r1

@r1 = 21.72 deg

horizontal is d1 from strike point where light strike at ice-water instersection,

d1 / 0.35 = tan21.72

d1 = 0.14 m

for ice to water :

1.31 sin21.72 = 1.33 sin@r2

@r2 = 21.38 deg

d2 / 1.50 = tan21.38

d2 = 0.587 m

d = d1 + d2 = 0.727 m