(i) A ray of light incident on face AB of an equilateral glass prism shows the minimum deviation of 30°. Calculate the speed of light through the prism.
(ii) Find the angle of incidence at face AB so that the emergent ray grazes along the face AC.
At the minimum deviation, the refracted ray inside the prism becomes parallel to its base.
Angle of minimum deviation is given as Dm = 30°
Since, the prism is equilateral, So, A = 60°
Refractive index of the prism
We know that μ = v1/v2
Hence the speed of light in prism would be 1/√2 times the speed of light in air i.e = 3 x108 /1.414 = 2.121 x108 m/s
(ii)
From Snell's law, we know that
For the emergent ray to graze at the face AC, the angle of refraction should be 90
So, applying snell's law at face AC, we get
From figure, we can see that angle of refraction at face AB is 15
So applying Snell's law we get
Sin iAB = sin rAB x μ12
or iAB = sin-1 (√sin 15°)