Question

A ray of light travels from a glass-to-liquid interface at an angle of 35.0º. Indices of refraction for the glass and liquid are, respectively, 1.52 and 1.63. What is the angle of refraction for the ray moving through the liquid?
a. 23.2º
b. 32.3º
c. 38.4º
d. 46.0º

Answer 1

Answer:

The angle of refraction for the ray moving through the liquid is = 32.3°

Explanation:

Refractive index of liquid (n₁/n₂) = sini/sinr

∴                 n₁/n₂ = sini/sinr ................ equation 1

n₁ = index of refraction for glass, n₂ = index of refraction for liquid

Where i = incident angle of the first medium, r = angle of refraction or angle in the second medium.

Since the light ray is traveling from glass - to - liquid,  the first medium is glass and the second medium is liquid. and the refractive index will be that liquid with respect to glass.

using the equation,

n₁/n₂ = sini/sinr

i = 35° , n₁ = 1.52, n₂= 1.63

Making sinr the subject of the equation above,

sinr = sini/(n₁/n₂)

sinr = sin35(1.52)/1.63

sinr =0.574(1.52)/1.63

sinr = 0.535

Taking the sin inverse of both side of the equation

sin⁻¹(sinr) = sin⁻¹(0.535)

∴ r = 32.3°

The angle of refraction for the ray moving through the liquid is = 32.3°

The right option is (b). 32.3°