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BITSAT 2023Paper 2
Exam
BITSAT
Year
2023
Paper
Paper 2
Subject
Physics
Chapter
Ray Optics

BITSAT 2023 · Paper 2 · Physics · Ray Optics

A thin prism P_1 with an angle 6^ ^ and made of glass of refractive...

A thin prism P1P_1 with an angle 6∘6^{{}^{\circ}} and made of glass of refractive index 1.54 is combined with another prism P2\mathrm{P}_2 made from glass of refractive index 1.72 to produce dispersion without average deviation. The angle of prism P2\mathrm{P}_2 is :

Options

  1. A6∘6^{{}^{\circ}}
  2. B1.3∘1.3^{{}^{\circ}}
  3. C7.8∘7.8^{{}^{\circ}}
  4. D4.5∘4.5^{{}^{\circ}}

Correct answer

D. 4.5∘4.5^{{}^{\circ}}

Step-by-step solution

Angle of deviation for first prism
δ1=A1(μ1−1)=6(1.54−1)\delta_1=A_1\left(\mu_1-1\right)=6(1.54-1)
Angle of deviation for second prism
δ2=A2(μ2−1)=A2(1.72−1)\begin{aligned} \\ & \delta_2=A_2\left(\mu_2-1\right) \\ \\ & =A_2(1.72-1) \\ \end{aligned}
For dispersion without deviation
δ1=δ2⇒6∘(1.54−1)=A2(1.72−1)⇒A2=6∘×0.540.72=18∘4=4.5∘\begin{aligned} \\ & \delta_1=\delta_2 \\ \\ & \Rightarrow 6^{{}^{\circ}}(1.54-1)=\mathrm{A}_2(1.72-1) \\ \\ & \Rightarrow \mathrm{A}_2=\frac{6^{{}^{\circ}} \times 0.54}{0.72}=\frac{18^{{}^{\circ}}}{4}=4.5^{{}^{\circ}} \\ \end{aligned}
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