Optics Question 948
Question: A horizontal ray of light passes through a prism of $ \mu =1.5 $ whose apex angle is $ 4{}^\circ $ and then strikes a vertical mirror M as shown. For the ray after reflection to become horizontal, the mirror must be rotated through an angle of:
Options:
A) $ 2^{o} $
B) $ {{3}^{o}} $
C) $ {{4}^{o}} $
D) $ {{1}^{o}} $
Show Answer
Answer:
Correct Answer: A
Solution:
[a] $ \delta =(\mu -1)A=(1.5-1)(4)=2^{o} $
$ i=\delta =2^{o} $
Let the mirror be rotated by an angle $ \theta $ so that $ i’=(2^{o}+\theta ) $
Then, $ {\delta _{total}}=180^{o} $
or $ \delta +180^{o}-2i’=180^{o} $
$ \therefore $ $ \delta =2i’ $
or $ {{2}^{\circ }}=2(2+\theta ) $
$ \theta =-2^{o} $
Here negative sign implies that $ i $ gets decreased or $ i’=0 $ i.e., light should fall normally on mirror.
