Question

# 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

Solution

( 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} )