A ray of light falls on one side of a prism whose refracting angle is 60°. Find the angle of incidence in order that the emergent ray may just graze the other side. $(μ = \frac{3}{2})$

Solution

Given,
Angle of prism, A = 60°
Angle of emergent ray, e =90^oRefractive index,

μ

\frac{3}{2}

∴ r₂ = C, the critical angle of the prism.

Now,

{}_{a}μ_{g} = \frac{1}{\sin C}

\Rightarrow

\sin C = \frac{1}{μ} = \frac{2}{3}

\Rightarrow

C = 41 ° 49'

Again,

A = r_{1} + r_{2}

\Rightarrow

r_{1} = A - r_{2} = 60 ° - 41 ° 49'

= 18 ° 11'

For refraction at the surface AB, we have

μ = \frac{\sin i}{\sin r_{1}} (Snell' s law)

\Rightarrow

\sin i = μ \sin r_{1}

= 1.5 \times \sin 18 ° 11' = 1.5 \times 0.3121 = 0.46815

i.e.,

i = 27 ° 55' .

is the required angle of incidence such that the emergent ray may just graze the other side.

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