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Standard IX

Physics

Total Internal Reflection

A light ray i...

Question

A light ray is incident at an angle $45^{o}$ with normal on a $10 c m$ thick plane slab of refractive index $n = 1.5$ . The lateral shift of the incident ray is ______ cm.

0.835

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8.35

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0.03

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1.197

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Solution

The correct option is C $0.03$
$\begin{matrix} G i v e n, t = 10 c m = .1 m \frac{sin i}{sin r_{1}} = R . I \frac{sin 45^{0}}{sin r_{1}} = 1.5 sin r_{1} = \frac{1}{\sqrt{2}} \times \frac{10}{1.5} = 0.4713 r_{1} = {sin}^{- 1} (0.4713) = 28^{0} 7^{'} α . s = \frac{0.1 sin (45 - {28.7}^{'})}{cos 28^{0} 7^{'}} = \frac{0.1 \times 0.2907}{0.8820} = 0.03 m \end{matrix}$

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A light ray is incident at an angle 45o with normal on a 10cm thick plane slab of refractive index n=1.5. The lateral shift of the incident ray is ______ cm.

The correct option is C 0.03Given,t=10cm=.1msinisinr1=R.Isin450sinr1=1.5sinr1=1√2×101.5=0.4713r1=sin−1(0.4713)=2807′α.s=0.1sin(45−28.7′)cos2807′=0.1×0.29070.8820=0.03m

A light ray is incident at an angle $45^{o}$ with normal on a $10 c m$ thick plane slab of refractive index $n = 1.5$ . The lateral shift of the incident ray is ______ cm.