A thin prism of angle 5° made of glass of refractive index μ 1=1.5 is combined with another prism of glass of refractive index μ 2=1.75 . The combination of the prisms produces dispersion without deviation. The angle of the second prism should be

Question

A thin prism of angle 5° made of glass of refractive index μ 1=1.5 is combined with another prism of glass of refractive index μ 2=1.75 . The combination of the prisms produces dispersion without deviation. The angle of the second prism should be (A) 5°  (B) 7°  (C) (10 ° /3) (D) 1.2°

Tardigrade Admin · Accepted Answer

For dispersion without deviation δ1+δ2=0 (μ1-1) mathrmA1+(μ2-1) mathrmA2=0 A2=-((μ1-1) A1/(μ2-1)) Substituting the given values, we get A 2=-((1 ⋅ 5 - 1) 5 ° /(1 ⋅ 75 - 1))=-(10 ° /3) The negative sign shows that the two prisms must be joined in opposition.

Q. A thin prism of angle $5^{\circ}$ made of glass of refractive index $μ_{1} = 1.5$ is combined with another prism of glass of refractive index $μ_{2} = 1.75$ . The combination of the prisms produces dispersion without deviation. The angle of the second prism should be

$5^{\circ}$

$7^{\circ}$

$\frac{1 0 ^{\circ}}{3}$

$1. 2^{\circ}$

Q. A thin prism of angle 5∘ made of glass of refractive index μ1​=1.5 is combined with another prism of glass of refractive index μ2​=1.75 . The combination of the prisms produces dispersion without deviation. The angle of the second prism should be

5∘

7∘

310∘​

1.2∘

For dispersion without deviation δ1​+δ2​=0 (μ1​−1)A1​+(μ2​−1)A2​=0 A2​=−(μ2​−1)(μ1​−1)A1​​ Substituting the given values, we get A2​=−(1⋅75−1)(1⋅5−1)5∘​=−310∘​ The negative sign shows that the two prisms must be joined in opposition.

Q. A thin prism of angle $5^{\circ}$ made of glass of refractive index $μ_{1} = 1.5$ is combined with another prism of glass of refractive index $μ_{2} = 1.75$ . The combination of the prisms produces dispersion without deviation. The angle of the second prism should be

$5^{\circ}$

$7^{\circ}$

$\frac{1 0 ^{\circ}}{3}$

$1. 2^{\circ}$