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

Option: 1

5.33^{\circ}


Option: 2

4^{\circ}


Option: 3

\mathrm{2.6^{\circ}}


Option: 4

3^{\circ}


Answers (1)

best_answer

For a thin prism, angle of minimum deviation is given by, \mathrm{\delta =(\mu -1)A}
where, \mathrm{\mu } is refractive index of the prism and \mathrm{A} is the angle of prism.
For dispersion without deviation,
\mathrm{\begin{aligned} & \quad \delta_1=\delta_2 \Rightarrow\left(\mu_1-1\right) \mathrm{A}_1=\left(\mu_2-1\right) \mathrm{A}_2 \\ & \Rightarrow \mathrm{A}_2=\frac{\left(\mu_1-1\right)}{\left(\mu_2-1\right)} \mathrm{A}_1 \\ & \text { Given, } \mu_1=1.54, \mathrm{~A}_1=4^{\circ}, \mu_2=1.72 \\ & \Rightarrow \mathrm{A}_2=\frac{(1.54-1)}{(1.72-1)} \times 4=3^{\circ} \end{aligned}}

Posted by

Ajit Kumar Dubey

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