Aray of light in air is incident upon a glass plate at an angle of 45°. the angle of refraction of the ray in the glass is 30°. what is the index of refraction of the glass?

Explanation:

Laws of  refraction:

(a) The incident ray, the refracted ray and the normal at the point of incident all lies in the same plane

(b) The ratio of the sine of incident  to the sine of refraction is a constant for a given pair of media, which is the refractive index of the second medium with respect to the first medium. The is also called Snell's law

from Snell's law,

Index of refraction of the glass = sini/sinr Equation 1

where i = incident angle, r = angle of refraction.

given: i = 45°, r = 30°

Substituting these values into equation 1,

Index of refraction of the glass = sin45°/sin30°

Index of refraction of the glass = (1/√2)/(1/2)

Index of refraction of the glass = 2/√2

Index of refraction of the glass = √2.

Therefore, The Index of refraction of the glass = √2.