Question

Calculate the angle of emergence (e) of the ray of light incident normally on the face AC of a glass prism ABC of refractive index `sqrt (3)`. How will the angle of emergence change qualitatively, if the ray of light emerges from the prism into a liquid of refractive index 1.3 instead of air?

Answer 1

According to Snell’s law:

μ₁ sin (i) = μ₂ sin (r)

μ_Prism = `sqrt 3`

μ_Prism = 30°

= sin (e)

`sqrt (3) xx 1/2` = sin (e)

e = 60°

Now, when the external medium is changed to a liquid of μ_L = 1.3, then,

`mu_"prism" sin (30)` = μ_L sin (e)

`sqrt (3) sin (30°)` = 1.3 Sin (e)

e = `sin^-1 (sqrt (3)/(2 xx 1.3))`

= 41.83°

Hence, the angle of emergence reduces to 41.83° from 60°.