Question

In winter a lake has a 0.20 m thick ice layer over 1.50 m of water. A light beam from above strikes a spot on the ice, making a 33 degree angle with the normal.

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

Answer 1

1*sin(33) = 1.31sinr

r = sin^-1(sin33/1.31) = 24.57 degrees

tan(24.57) = d/0.2

displacement in the ice d = 0.091 m

again use snells law

ice to water surface

1.31sin(24.57) = 1.33sinr'

r' = 24.17 degrees

displacement in water d' = 1.5tan(24.17) = 0.673 m

total displacement D = d+d' = 0.091+0.673 = 0.764 m