A thin prism P1 with an angle 6° and made of glass of refractive index 1.54 is combined with another prism P2 made from glass of refractive index 1.72 to produce dispersion without average deviation. The angle of prism P2 is

Question

A thin prism P1 with an angle 6° and made of glass of refractive index 1.54 is combined with another prism P2 made from glass of refractive index 1.72 to produce dispersion without average deviation. The angle of prism P2 is (A) 7.8° (B) 4.5° (C) 6 circ (D) 1.3°

Tardigrade Admin · Accepted Answer

δ1= δ2 [for no average deviation] ⇒ 6°(1.54-1)= A (1.72-1) ⇒ A =(6° × 0.54/0.72) =(18°/4)=4.5°

Q. A thin prism $P_{1}$ with an angle $6^{\circ}$ and made of glass of refractive index $1.54$ is combined with another prism $P_{2}$ made from glass of refractive index $1.72$ to produce dispersion without average deviation. The angle of prism $P_{2}$ is

$7. 8^{\circ}$

$4. 5^{\circ}$

$6^{c i rc}$

$1. 3^{\circ}$

$δ_{1} = δ_{2}$ [for no average deviation]
$\Rightarrow 6^{\circ} (1.54 - 1) = A (1.72 - 1)$
$\Rightarrow A = \frac{6 ^{\circ} \times 0.54}{0.72}$
$= \frac{1 8 ^{\circ}}{4} = 4. 5^{\circ}$

Q. A thin prism P1​ with an angle 6∘ and made of glass of refractive index 1.54 is combined with another prism P2​ made from glass of refractive index 1.72 to produce dispersion without average deviation. The angle of prism P2​ is

7.8∘

4.5∘

6 circ

1.3∘