Question

A beam of light is incident from air on the surface of aliquid. If the angle of incidence is 40.0° and the angle ofrefraction is 31.0°, find the critical angle for the liquidwhen surrounded by air.
1°
b) A light ray, traveling in air, strikes the surface of abeaker of mineral oil at an angle of 37.5o with thenormal to the surface. The speed of light in mineral oil is 2.17 x108 m/s.. Calculate the angle of refraction.
1o

Answer 1

Answer:

a) 53.3o b) 26.12o

Explanation:

Using Snell's law, the critical angle can be calculated. Critical angle is the maximum angle of incidence when light travels from  a denser medium to a less dense medium that produces angle of refraction of 90o

n ( refractive index of the oil) = sin i/ sin r

i (incidence angle) = 40o

r (angle of refraction) = 31o

n = sin 40 / sin 31 ) = 1.248

critical angle = sin^-1 ( nr/ni) and nr = 1 ( refractive index of air)

critical angle = sin^-1 (1/1.248) = 53.5o

b) sin i / sin r = speed of light in air (v1 m/s) / speed of light in the medium (v2 m/s)

sin^-1((sin i × v2) / v1) = r

r = sin^-1 ( (sin 37.5 × 2.17 ×10^8) / 3.0 × 10^8) = 26.12o