Ray Optics and Optical Instruments - Result Question 53
55. A thin prism having refracting angle $10^{\circ}$ is made of glass of refractive index 1.42. This prism is combined with another thin prism of glass of refractive index 1.7. This combination produces dispersion without deviation. The refracting angle of second prism should be
(a) $6^{\circ}$
(c) $10^{\circ}$
(b) $8^{\circ}$
(d) $4^{\circ}$
[2017]
Show Answer
Answer:
Correct Answer: 55. (a)
Solution:
- (a) For dispersion without deviation
$(\mu-1) A_1+(\mu^{\prime}-1) A_2=0$
$|(\mu-1) A_1|=|(\mu^{\prime}-1) A_2|$
$(1.42-1) \times 10^{\circ}=(1.7-1) A_2$
$4.2=0.7 A_2$
$A_2=6^{\circ}$
In case of deviation without dispersion
$ \frac{A^{\prime}}{A^{\prime}}=\frac{(\mu_V-\mu_R)}{(\mu_V^{\prime}-\mu_R^{\prime})} $
