Ray Optics and Optical Instruments - Result Question 60
63. A thin prism of angle $15^{\circ}$ made of glass of refractive index $\mu_1=1.5$ is combined with another prism of glass of refractive index $\mu_2=1.75$. The combination of the prism produces dispersion without deviation. The angle of the second prism should be
(a) $7^{\circ}$
(b) $10^{\circ}$
(c) $12^{\circ}$
(d) $5^{\circ}$
[2011M]
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Answer:
Correct Answer: 63. (b)
Solution:
- (b) Deviation $=$ zero
So, $\delta=\delta_1+\delta_2=0$
$\Rightarrow(\mu_1-1) A_1+(\mu_2-1) A_2=0$
$\Rightarrow A_2(1.75-1)=-(1.5-1) 15^{\circ}$
$\Rightarrow A_2=-\frac{0.5}{0.75} \times 15^{\circ}$
or $A_2=-10^{\circ}$.
Negative sign shows that the second prism is inverted with respect to the first.
