| 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 \[0\le x\le d\,\,\left( 1-\frac{1}{{{\mu }_{0}}} \right)\] 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: |
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A) \[d\,(1-\sin \theta )\]
B) \[d\,(1-\cos \theta )\]
C) \[d\,\sin \theta \]
D) \[d\,\cos \theta \]
Correct Answer: B
Solution :
Snell?s law \[={{\mu }_{0}}\sin \,(90{}^\circ -\theta )={{\mu }_{0}}\left( 1+\frac{x}{d} \right)\,\sin 90{}^\circ \] \[\Rightarrow \] \[\left( 1+\frac{x}{d} \right)=\cos \theta \] \[\Rightarrow \] \[x=d\,(1-\cos \theta )\]
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