Monochromatic light is incident on a glass prism of angle A. If the refractive index of the material of the prism is μ, a ray, incident at an angle θ, on the face AB would get transmitted through the face AC of the prism provided :

Engineering

Physics

Prism

Question

$θ > \cos^{- 1} [μ \sin (A + \sin^{- 1} (\frac{1}{μ}))]$

$θ > \sin^{- 1} [μ \sin (A - \sin^{- 1} (\frac{1}{μ}))]$

$θ < \sin^{- 1} [μ \sin (A - \sin^{- 1} (\frac{1}{μ}))]$

$θ < \cos^{- 1} [μ \sin (A + \sin^{- 1} (\frac{1}{μ}))]$

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1 sin $θ$ = m sin $ϕ$

m sin f < 1

A – α = $ϕ$ < sin–1 $(\frac{1}{μ})$

A – α sin^–1 $(\frac{1}{μ}) < α$

$μ \sin (A - \sin^{- 1} (\frac{1}{μ}))$

< m sin α = sin $ϕ$