A thin prism having refracting angle 10^ is made of glass of refractive index 1.42 . This prism is combined wi

Question

A thin prism having refracting angle 10^ is made of glass of refractive index 1.42 . This prism is combined with another thin prism of glass of refractive index 1.7 . This combination produces dispersion without deviation. The refracting angle of the second prism should be:

Accepted Answer

For dispersion without deviation, the net deviation produced by the combination must be zero:

δ_{net} = δ_{1} + δ_{2} = 0

For a thin prism,

δ = (μ - 1) A

.

(μ_{1} - 1) A_{1} + (μ_{2} - 1) A_{2} = 0

Given

A_{1} = 1 0^{\circ}

,

μ_{1} = 1.42

, and

μ_{2} = 1.7

:

(1.42 - 1) 1 0^{\circ} + (1.7 - 1) A_{2} = 0

0.42 \times 1 0^{\circ} + 0.7 A_{2} = 0

4.2 = - 0.7 A_{2}

∣ A_{2} ∣ = \frac{4.2}{0.7} = 6^{\circ}

The magnitude of the refracting angle of the second prism is

6^{\circ}

.

A thin prism having refracting angle $1 0^{\circ}$ is made of glass of refractive index $1.42$ . This prism is combined with another thin prism of glass of refractive index $1.7$ . This combination produces dispersion without deviation. The refracting angle of the second prism should be:

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A thin prism having refracting angle 10∘ is made of glass of refractive index 1.42. This prism is combined with another thin prism of glass of refractive index 1.7. This combination produces dispersion without deviation. The refracting angle of the second prism should be: