Question

As shown in the figure, thin prisms P₁ and P₂ are combined to produce dispersion without deviation. For prism P₁, angle of prism is 4° and refractive index is 1.54. For prism P₂ angle of prism is 3°. Refractive index of material of P2 is _______ .
(A) 1.72
(B) 1.5
(C) 2.4
(D) 0.58

Answer 1

we know, , $\bf{\delta=(\mu-1)A}$
$\delta$ is the deviation angle and A is angle of prism.

for without deviation ,
$\delta_1=\delta_2$

$(\mu_1-1)A_1=(\mu_2-1)A_2$

(1.54 - 1) × 4° = $(\mu_2-1)\times3^{\circ}$

0.54 × 4°/3°= $(\mu_2-1)$

$\mu_2-1$ = 0.54 × 4°/3° = 0.18 × 4

$\mu_2$ = 0.72 + 1 = 1.72

hence, refractive index of P2 is 1.72
option (A) is correct.