A rectangular glass wedge is partially dipped in water \[\left( {{n}_{\text{glass}}}=\frac{3}{2} \right).\]A beam of light entering face AB normally reaches entirely to AC. |
Now, value of angle a must be |
A) less than \[60{}^\circ \]
B) less than \[30{}^\circ \]
C) more than \[60{}^\circ \]
D) between\[30{}^\circ \]to \[60{}^\circ \]
Correct Answer: C
Solution :
Beam reaches AC, if TIR occurs at BC. |
From geometry of figure, angle of incidence over face \[BC=\alpha .\] |
For beam to reach AC, |
\[\sin \alpha >\frac{{{n}_{2}}}{{{n}_{1}}}\] |
where, \[{{n}_{2}}=\]refractive index of water \[=\frac{4}{3}\] and \[{{n}_{1}}=\]refractive index of glass \[=\frac{3}{2}.\] |
\[\therefore \]\[\sin \alpha >\frac{\frac{4}{3}}{\frac{3}{2}}\]\[\Rightarrow \]\[\sin \alpha >\frac{8}{9}=0.89\] |
\[\therefore \]\[\alpha >60{}^\circ \] |
\[\therefore \]\[\sin 60{}^\circ \approx 0.86\] |
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