For a transparent prism, if the angle of minimum deviation is equal to its refracting angle, the refractive index n of the prism satisfies [2026]

Question

For a transparent prism, if the angle of minimum deviation is equal to its refracting angle, the refractive index $n$ of the prism satisfies [2026]

Smart Achievers · Accepted Answer

(2)

$δ_{\min} = 2 i - A \Rightarrow i = δ_{\min} = A$

$Also, μ = \frac{\sin (\frac{δ_{\min} + A}{2})}{\sin (\frac{A}{2})}$

$\Rightarrow μ = \frac{\sin A}{\sin \frac{A}{2}} = 2 \cos (\frac{A}{2})$

$1 < μ < 2 . . . (1)$

$δ_{\min} = 2 i - A$

$A = 2 i - A \Rightarrow i = A$

$i < 90 ° (grazing incidence)$

$A < 90 °$

$μ = 2 \cos (\frac{A}{2}), A < 90 °$

$μ > \sqrt{2} . . . (2)$

$from (1) & (2)$

$\sqrt{2} < μ < 2$

Solution

Q.
For a transparent prism, if the angle of minimum deviation is equal to its refracting angle, the refractive index $n$ of the prism satisfies [2026]

1 $\sqrt{2} < n < 2 \sqrt{2}$

2 $\sqrt{2} < n < 2$

3 $n \geq 2$

4 $1 < n < 2$

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Solution

Q. For a transparent prism, if the angle of minimum deviation is equal to its refracting angle, the refractive index n of the prism satisfies [2026]

1 2<n<22

2 2<n<2

3 n≥2

4 1<n<2