A ray of light incident normally on the horizontal face of the slab and just fail to emerge from the diagonal face of the prism. If prism angle is $30^{o}$ then refractive index of the prism can be

$\sqrt{3}$
slightly greater than 2
$\sqrt{2}$
slightly less than 2

Question

A ray of light incident normally on the horizontal face of the slab and just fail to emerge from the diagonal face of the prism. If prism angle is $30^{o}$ then refractive index of the prism can be

$\sqrt{3}$
slightly greater than 2
$\sqrt{2}$
slightly less than 2

Toppr Admin · Accepted Answer

For the ray to graze on the face AC- -xA0-i-e- e-90oFrom geometry- -x3B8-c-30oLet the refractive index of the prism be -x3BC-Snell-apos- law- -xA0-x3BC-o-xD7-sin30o-1-xD7-1-x27F9-x3BC-o-2For total internal to occur- means -x3B8-gt-x3B8-c-x27F9-x3BC-o-lt-2

A ray of light incident normally on the horizontal face of the slab and just fail to emerge from the diagonal face of the prism. If prism angle is 30o then refractive index of the prism can be√3slightly greater than 2√2slightly less than 2

For the ray to graze on the face AC, i-e, e=90oFrom geometry, θc=30oLet the refractive index of the prism be μ.Snell' law, μo×sin30o=1×1⟹μo=2For total internal to occur, means θ>θc⟹μo<2

A ray of light incident normally on the horizontal face of the slab and just fail to emerge from the diagonal face of the prism. If prism angle is $30^{o}$ then refractive index of the prism can be

$\sqrt{3}$
slightly greater than 2
$\sqrt{2}$
slightly less than 2

For the ray to graze on the face AC, i-e, $e = 90^{o}$

From geometry, $θ_{c} = 30^{o}$

Let the refractive index of the prism be $μ$ .

Snell' law, $μ_{o} \times s i n 30^{o} = 1 \times 1$

$⟹ μ_{o} = 2$

For total internal to occur, means $θ > θ_{c}$

$⟹ μ_{o} < 2$