Sum

Two prisms of identical geometrical shape are combined with their refracting angles oppositely directed. The materials of the prisms have refractive indices 1.52 and 1.62 for violet light. A violet ray is deviated by 1.0° when passes symmetrically through this combination. What is the angle of the prisms?

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#### Solution

Let A be the angle of the prisms.

Refractive indices of the prisms for violet light, μ_{1} = 1.52 and μ_{2} = 1.62

Angle of deviation, δ = 1.0°

As the prisms are oppositely directed, the angle of deviation is given by

δ = (μ_{2} − 1)A − (μ_{1} − 1)A

δ = (μ_{2} −μ_{1} )A

\[A = \frac{\delta}{\mu_2 - \mu_1} = \frac{1}{(1 . 62) - (1 . 52)} = \frac{1}{0 . 1}\]

\[ \Rightarrow A = 10^\circ\]

So, the angle of the prisms is 10^{∘}.

Concept: Dispersion by a Prism

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