A ray of light is travelling from air enters a liquid at an angle of 45 degree with the normal. If the corresponding angle of refraction is 30 degree, then what is the refractive index of the liquid with respect to air.
Answers
Answer : the refractive index of the liquid with respect to air is √2
Given: ray enters at an angle of 45°, get refracted at an angle of 30°
To find: refractive index of the liquid with respect to air
Solution: we are given an angle of incidence that is 45° and an angle of refraction that is 30° with the normal
here we will apply snell's law.
Snell's law gives a relation between the refractive indexes of two surfaces that a ray of light crosses and a path that the ray of light takes.
we can write it as
n1 sin i = n2 sin r
here n1 and n2 are refractive index and i is the incident angle, r is refracted angle
According to the question
n1 = 1
i = 45°
r = 30°
putting the values in the equation
sin45° = n2 × sin30°
n2 = (1/√2)/1/2
n2 = √2 = 1.414
Therefore, the refractive index of the liquid with respect to air is 1.414.