A prism of refractive index √2 has a refracting angle of 60°. At what angle must a ray be incident on it so that it suffers a minimum deviation?

Question

A prism of refractive index √2 has a refracting angle of 60°. At what angle must a ray be incident on it so that it suffers a minimum deviation? (A) 30° (B) 45° (C) 60° (D) 75°

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/78b66f1297753d00be0eabd253aa464c-.png" /> μ=√2, A=60° At for minimum deviation: i=ie and r1=r2 Also, r1+r2=A or 2 r=60° r=30° μ=( sin i/ sin r) √2=2 sin i [. Putting .r=30°] sin i=(1/√2) i=45°

Q. A prism of refractive index $2$ has a refracting angle of $6 0^{\circ}$ . At what angle must a ray be incident on it so that it suffers a minimum deviation?

$3 0^{\circ}$

$4 5^{\circ}$

$6 0^{\circ}$

$7 5^{\circ}$

$μ = 2, A = 6 0^{\circ}$
At for minimum deviation:
$i = i_{e}$ and $r_{1} = r_{2}$
Also, $r_{1} + r_{2} = A$
or $2 r = 6 0^{\circ}$
$r = 3 0^{\circ}$
$μ = \frac{s i n i}{s i n r}$
$2 = 2 sin i$
$[$ Putting $r = 3 0^{\circ}]$
$sin i = \frac{1}{2}$
$i = 4 5^{\circ}$

Q. A prism of refractive index 2​ has a refracting angle of 60∘. At what angle must a ray be incident on it so that it suffers a minimum deviation?

30∘

45∘

60∘

75∘