A thin prism $\mathrm{P}_1$ with angle $4^{\circ}$ made of glass having refractive index 1.54 , is combined with another thin prism $\mathrm{P}_2$ made of glass having refractive index 1.72 to get dispersion without deviation. The angle of the prism $\mathrm{P}_2$ in degrees is
Solution
<p>We know, for thin prism,</p>
<p>$\mu = {{A + \delta } \over A}$</p>
<p>where, $\mu$ = refractive index</p>
<p>A = Angle of prism</p>
<p>$\delta$ = Angle of deviation</p>
<p>We can write, $\mu A = A + \delta$</p>
<p>$\Rightarrow \delta = (\mu - 1)A$</p>
<p>given, ${\delta _{net}} = 0$</p>
<p>$\Rightarrow ({\mu _1} - 1){A_1} - ({\mu _2} - 1){A_2} = 0$</p>
<p>$\Rightarrow (1.54 - 1)4 - (1.72 - 1){A_2} = 0$</p>
<p>$\Rightarrow {A_2} = {{54 \times 4} \over {72}} \Rightarrow {A_2} = 3^\circ$</p>
About this question
Subject: Physics · Chapter: Optics · Topic: Reflection and Mirrors
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