A Ray of light in air makes an angle of 45 degree at the surface of a sheet of ice . the ray is refracted within the Ice at an angle of 30 degree . a) what is the critical angle for the Ice? b) A speck of dirt is embedded 2CM below the surface of the Ice . what is the Apparent depth when viewed at normal incidence

Explanation:

a )

Refractive index of ice = sini / sin r where i is angle of incidence and r is angle of refraction

angle of incidence = 90 - 45 = 45

angle of refraction = 30

refractive index of ice   μ  = sin 45 / sin 30

= 2/ √2

μ  = √2 = 1.414

μ  = 1 / sin C where C is critical angle for ice - air interface

sinC = 1 / μ

= 1 / 1.414

= .70

C = 44 .42° .

b )

real depth / apparent depth = refractive index

2 / apparent depth = 1.414

apparent depth = 2 / 1.414

= 1.414 cm .