MHT CET · Physics · Ray Optics
A thin prism \(\mathrm{P}_{1}\) with angle \(4^{\circ}\) and made from glass of refractive index \(1 \cdot 54\) is
combined with another thin prism \(\mathrm{P}_{2}\) made from glass of refractive index \(1 \cdot 72\) to
produce dispersion without deviation. The angle of prism for \(\mathrm{P}_{2}\) is
- A \(4^{\circ}\)
- B \(5 \cdot 33^{\circ}\)
- C \(2 \cdot 6^{\circ}\)
- D \(3^{\circ}\)
Answer & Solution
Correct Answer
(D) \(3^{\circ}\)
Step-by-step Solution
Detailed explanation
For thin prism the angle of deviation \(\delta=\mathrm{A}(\mathrm{n}-1)\)
\(\therefore \delta_{1}=\delta_{2} \quad\) for no deviation
\(\therefore A_{1}\left(n_{1}-1\right)=A_{2}\left(n_{2}-1\right)\)
\(4(1.54-1)=\mathrm{A}_{2}(1.72-1)\)
\(\therefore 4 \times 0.54=\mathrm{A}_{2} \times 0.72\)
\(\mathrm{A}_{2}=\frac{4 \times 0.54}{0.72}=3^{\circ}\)
\(\therefore \delta_{1}=\delta_{2} \quad\) for no deviation
\(\therefore A_{1}\left(n_{1}-1\right)=A_{2}\left(n_{2}-1\right)\)
\(4(1.54-1)=\mathrm{A}_{2}(1.72-1)\)
\(\therefore 4 \times 0.54=\mathrm{A}_{2} \times 0.72\)
\(\mathrm{A}_{2}=\frac{4 \times 0.54}{0.72}=3^{\circ}\)
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