A) \[60{}^\circ 48\]
B) \[64{}^\circ 48\]
C) \[74{}^\circ 48\]
D) None of these
Correct Answer: B
Solution :
Key Idea: When ray passes from denser to rarer medium, angle of refraction is greater than angle of incidence. When a ray of light passes from glycerine (denser,\[\mu =1.47\]) to water (rarer,\[\mu =1.33\]) the angle of refraction (r) is greater than angle of incidence (i), than from Snells law \[\frac{\sin i}{\sin r}=\frac{{{\mu }_{2}}}{{{\mu }_{1}}}<1\] When \[r={{90}^{o}},\]corresponding angle of incidence is known as critical angle i.e., \[i={{\theta }_{c}}.\] \[\therefore \] \[\frac{\sin {{\theta }_{c}}}{\sin {{90}^{o}}}=\frac{{{\mu }_{2}}}{{{\mu }_{1}}}\] \[\Rightarrow \] \[\sin {{\theta }_{c}}=\frac{{{\mu }_{2}}}{{{\mu }_{1}}}\] \[\Rightarrow \] \[{{\theta }_{c}}={{\sin }^{-1}}\left( \frac{{{\mu }_{2}}}{{{\mu }_{1}}} \right)\] \[={{\sin }^{-1}}\left( \frac{1.33}{1.47} \right)\] \[{{\theta }_{c}}={{64}^{o}}\,48.\]
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