Question

$A rectangular glass slab ABCD of refractive index n1, is immersed in water of refractive index n2(n1>n2). A ray of light is incident at the surface AB of the slab as$

A rectangular glass slab ABCD of refractive index ( n_{1}, ) is immersed in water of refractive index ( n_{2}left(n_{1} > n_{2}right) . ) A ray of light is incident at the surface ( mathrm{AB} ) of the slab as shown. The maximum value of the angle of incident ( alpha_{text {max }} ), such that the ray comes out only from the other surface ( mathrm{CD} ) is given by

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Physics

Solution

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$A rectangular glass slab ABCD of refractive index n1, is immersed in water of refractive index n2(n1>n2). A ray of light is incident at the surface AB of the slab as shown. The maximum value of the angle of incident αmax , such that the ray comes out only from the other surface CD is given by$

( frac{n_{1}}{n_{2}}=frac{sin alpha_{text {nuare }}}{sin gamma_{1}} )
( Rightarrow quad alpha_{n a}=sin ^{-1}left[frac{n_{1}}{n_{n}} sin gamma_{1}right]-(i) )
2) Also ( r,+r_{1} Rightarrow 0 )
Hence ( begin{aligned} alpha operatorname{mex} &=sin ^{-1}left[frac{n_{1}}{n_{2}} sin left{90^{prime}-sin ^{-1}left(frac{n_{2}}{n}right)right}right. &=sin ^{-1}left[frac{n_{1}}{n_{2}} cos left{sin ^{-1}left(frac{n_{2}}{n_{1}}right)right]right] end{aligned} )