# Q 9.22  At what angle should a ray of light be incident on the face of a prism of refracting angle $60^{\circ}$ so that it just suffers total internal reflection at the other face? The refractive index of the material of the prism is $1.524$.

P Pankaj Sanodiya

Let prism be ABC ,

as emergent angle $e=90^0$,

$\mu_{glass}sinr_2 = 1sin90$

$sinr_2=\frac{1}{1.524} = 0.6562$

$r_2= 41 ^0$ (approx)

Now as we know in the prism

$r_1+r_2=A$

Hence, $r_1+=A-r_2=60-41=19^0$

Now applying snells law at surface AB

$1sini=\mu _{glass}sinr_1$

$sini=1.524sin19$

$sini=0.496$

$i = 29.75^0$

Hence the angle of incident is 29.75 degree.

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