Question

a beam of light passes from air into a substance X. if the angle of incidence be 72° and the angle of refraction be 40°, find refractive index.​

Answer 1

Answer:

According to snell's law,

the ratio of sine of angle of incidence to the sine of angle of refraction is constant for a given pair of media (such as 'air and glass' or 'air and water'). That is:

$\displaystyle\sf\:\:\:\:\;\:\: :\mapsto \dfrac{\textsf{\textbf{sine of angle of incidence}}}{\textsf{\textbf{sine of angle of refraction}}} = \sf constant$

$\displaystyle\sf\:\:\;\:\:\:\: :\mapsto \dfrac{\bf sin\:i}{\bf sin\:r} = \sf constant$

Here, angle of incidence = 72°

Angle of refraction = 40°

So,

$\displaystyle\sf\:\:\;\:\:\:\: :\longrightarrow n = \dfrac{sin72^{\circ}}{sin40^{\circ}}$

$\displaystyle\sf\:\:\;\:\:\:\: :\longrightarrow n = \dfrac{0.951}{0.642}$

$\displaystyle\sf\:\:\;\:\:\:\: \therefore n = 1.48$

Thus, the refractive index of substance X is 1.48.