A prism having refractive index 1.414 and refracting angle $30^{\circ}$ has one of the refer A prism having refractive index 1.414 and refracting angle $30^{\circ}$ has one of the referacting surface silvered. A beam of light incident on the other refracting surface will retrace its path, if the angle of incidence is acting surface silvered. A beam of light incident on the other refracting surface will retrace its path, if the angle of incidence is

0^{\circ}

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30^{\circ}

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60^{\circ}

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45^{\circ}

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Solution

The correct option is D $45^{\circ}$
At second surface, there is no refraction so
$r_{2} = 0$
$∴ r_{1} = A = 30^{\circ}$
From snell's law
$n = \frac{s i n i_{1}}{s i n r_{1}}$
$n = \frac{s i n i_{1}}{s i n 30^{\circ}}$
$s i n i_{1} = \sqrt{2} \times \frac{1}{2} = \frac{1}{\sqrt{2}}$
$s i n i_{1} = \frac{1}{\sqrt{2}}$
$i_{1} = 45^{\circ}$ .

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The correct option is D 45∘At second surface, there is no refraction so r2=0 ∴r1=A=30∘ From snell's law n=sin i1sin r1 n=sin i1sin 30∘ sin i1=√2×12=1√2 sin i1=1√2 i1=45∘.