A certain prism produces a minimum deviation of 42°. It produces a deviation of 45° when the angle of incidence is either 43° or 62°. The angle of incidence when the prism undergoes minimum deviation is

Question

A certain prism produces a minimum deviation of 42°. It produces a deviation of 45° when the angle of incidence is either 43° or 62°. The angle of incidence when the prism undergoes minimum deviation is (A) 60° (B) 30° (C) 49° (D) 51°

Tardigrade Admin · Accepted Answer

δ=i+e-A ⇒ 45=43+62-A Or A=43+62-45=60° D min =2 i-A or i=(A+A/2)=(60+42/2)=51°

Q. A certain prism produces a minimum deviation of $4 2^{\circ}$ . It produces a deviation of $4 5^{\circ}$ when the angle of incidence is either $4 3^{\circ}$ or $6 2^{\circ}$ . The angle of incidence when the prism undergoes minimum deviation is

$6 0^{\circ}$

$3 0^{\circ}$

$4 9^{\circ}$

$5 1^{\circ}$

$4 0^{\circ}$

$δ = i + e - A$
$\Rightarrow 45 = 43 + 62 - A$
Or $A = 43 + 62 - 45 = 6 0^{\circ}$
$D_{m i n} = 2 i - A$
or $i = \frac{A + A}{2} = \frac{60 + 42}{2} = 5 1^{\circ}$

Q. A certain prism produces a minimum deviation of 42∘. It produces a deviation of 45∘ when the angle of incidence is either 43∘ or 62∘. The angle of incidence when the prism undergoes minimum deviation is

60∘

30∘

49∘

51∘

40∘

δ=i+e−A ⇒45=43+62−A Or A=43+62−45=60∘ Dmin​=2i−A or i=2A+A​=260+42​=51∘