Optics 4 Question 12
12. A thin prism $P _1$ with angle $4^{\circ}$ and made from glass of refractive index 1.54 is combined with another thin prism $P _2$ made from glass of refractive index 1.72 to produce dispersion without deviation. The angle of the prism $P _2$ is
(a) $5.33^{\circ}$
(b) $4^{\circ}$
(c) $3^{\circ}$
(d) $2.6^{\circ}$
(1990, 2M)
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Answer:
Correct Answer: 12. (c)
Solution:
- Deviation $\delta=(\mu-1) A$
Given, $\delta _{\text {net }}=0$
$$ \begin{aligned} & \therefore \quad\left(\mu _1-1\right) A _1=\left(\mu _2-1\right) A _2 \\ & \text { or } \\ & A _2=\frac{\left(\mu _1-1\right)}{\left(\mu _2-1\right)} A _1=\frac{(1.54-1)}{(1.72-1)}\left(4^{\circ}\right)=3^{\circ} \end{aligned} $$
