A thin prism P1 with angle 4° and made from glass of refractive index 1.54 is combined with another thin prism P2 made from glass of refractive index 1.72 to produce dispersion without deviation. The angle of the prism P2 is

Question

A thin prism P1 with angle 4° and made from glass of refractive index 1.54 is combined with another thin prism P2 made from glass of refractive index 1.72 to produce dispersion without deviation. The angle of the prism P2 is (A) 5.33° (B) 4° (C) 3° (D) 2.6°

Tardigrade Admin · Accepted Answer

Deviation δ =(μ-1)A Given δnet=0 ∴ (μ1-1)A1=(μ2-1)A2 or A2=((μ-1)/(μ2-1))A1 =((1.54-1)/(1.72-1))(4°)=3° ∴ Correct option is (c).

Q. A thin prism $P_{1}$ with angle $4^{\circ}$ and made from glass of refractive index 1.54 is combined with another thin prism $P_{2}$ made from glass of refractive index 1.72 to produce dispersion without deviation. The angle of the prism $P_{2}$ is

$5.3 3^{\circ}$

$4^{\circ}$

$3^{\circ}$

$2. 6^{\circ}$

Deviation $δ = (μ - 1) A$
Given $δ_{n e t} = 0$
$∴ (μ_{1} - 1) A_{1} = (μ_{2} - 1) A_{2}$
$or A_{2} = \frac{( μ - 1 )}{( μ _{2} - 1 )} A_{1}$
$= \frac{( 1.54 - 1 )}{( 1.72 - 1 )} (4^{\circ}) = 3^{\circ}$
$∴$ Correct option is (c).

Q. A thin prism P1​ with angle 4∘ and made from glass of refractive index 1.54 is combined with another thin prism P2​ made from glass of refractive index 1.72 to produce dispersion without deviation. The angle of the prism P2​ is

5.33∘

4∘

3∘

2.6∘