The refractive index of the material of a prism is $\sqrt{2}$ and the angle of the prism is $30^{0}$ . One of the two refracting surfaces of the prism is made a mirror facing inwards by silver coating. A beam of monochromatic light entering the prism from the other face will retrace its path (after reflection from the silvered surface), if its angle of incidence on the prism is

Question

The refractive index of the material of a prism is

\sqrt{2}

and the angle of the prism is

30^{0}

. One of the two refracting surfaces of the prism is made a mirror facing inwards by silver coating. A beam of monochromatic light entering the prism from the other face will retrace its path (after reflection from the silvered surface), if its angle of incidence on the prism is

Toppr Admin · Accepted Answer

Using A-r1-r230-r1-0so r1-30Using Snell-apos-s Law-xA0- 1-xD7-sini-x3BC-xD7-sinr1-xD7-sini-x221A-2-xD7-sin30-x221A-23-2sini-1-x221A-2i-45ooption 4 is correct

Using A=r1+r230=r1+0so r1=30Using Snell's Law, 1×sini=μ×sinr1×sini=√2×sin30=√23/2sini=1/√2i=45ooption 4 is correct

Using $A = r_{1} + r_{2}$

$30 = r_{1} + 0$

so $r_{1} = 30$

Using Snell's Law, $1 \times s i n i = μ \times s i n r$

$1 \times s i n i = \sqrt{2} \times s i n 30 = \sqrt{2} 3 / 2$

$s i n i = 1 / \sqrt{2}$

$i = 45^{o}$

option 4 is correct