| A ray hits the y-axis making an angle \[\theta \] with y-axis as shown in the figure. The variation of refractive index with x-coordinate is \[\mu ={{\mu }_{0}}\left( 1-\frac{x}{d} \right)\] for \[0\le \times \le d\left( 1-\frac{1}{{{\mu }_{0}}} \right)\] and \[\mu ={{\mu }_{0}}\] for \[x<0\] where d is a positive constant. The maximum x-coordinate of the path traced by the ray is |
 |
A) \[d(1-\sin \theta )\]
B) \[d(1-\cos \theta )\]
C) \[d\,\,\sin \theta \]
D) \[d\,\,\cos \theta \]
Correct Answer: A
Solution :
| [a] Snell?s law \[={{\mu }_{0}}\sin \,(90{}^\circ -\theta )={{\mu }_{0}}\left( 1-\frac{x}{d} \right)\] |
| \[\sin 90{}^\circ \Rightarrow \left( 1-\frac{x}{d} \right)=\cos \theta \Rightarrow x=d(1-\cos \theta )\] |
You need to login to perform this action.
You will be redirected in
3 sec
