| 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: |
 |
A) \[{{2}^{o}}\]
B) \[{{3}^{\text{o}}}\]
C) \[{{4}^{\text{o}}}\]
D) \[{{1}^{\text{o}}}\]
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. |
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