Angle of prism is $30^{\circ}$ and its refractive index is $\sqrt{2}$ and one of the refracting faces is silvered. At what angle of incidence, a ray should be incident on one surface so that after reflection from the silvered surface, it retraces its path

30^{\circ}

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60^{\circ}

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45^{\circ}

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s i n^{- 1} \sqrt{1.5}

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Solution

The correct option is C $45^{\circ}$
$r_{1} = A r_{2} = 0 μ = \frac{s i n i_{1}}{s i n r_{2}} = \frac{s i n i}{s i n 30} S i n i = μ s i n 30 = \sqrt{2} \times \frac{1}{2} A + 90 + 90 - r_{1} = 180 S i n i = \frac{1}{\sqrt{2}} A = r_{1} = 30^{\circ} i = 45^{\circ}$

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Angle of prism is 30∘ and its refractive index is √2 and one of the refracting faces is silvered. At what angle of incidence, a ray should be incident on one surface so that after reflection from the silvered surface, it retraces its path

The correct option is C 45∘r1=Ar2=0μ=sini1sinr2=sinisin30Sini=μsin30=√2×12A+90+90−r1=180Sini=1√2A=r1=30∘i=45∘

Angle of prism is $30^{\circ}$ and its refractive index is $\sqrt{2}$ and one of the refracting faces is silvered. At what angle of incidence, a ray should be incident on one surface so that after reflection from the silvered surface, it retraces its path

The correct option is C $45^{\circ}$
$r_{1} = A r_{2} = 0 μ = \frac{s i n i_{1}}{s i n r_{2}} = \frac{s i n i}{s i n 30} S i n i = μ s i n 30 = \sqrt{2} \times \frac{1}{2} A + 90 + 90 - r_{1} = 180 S i n i = \frac{1}{\sqrt{2}} A = r_{1} = 30^{\circ} i = 45^{\circ}$