question_answer

When a ray of light enters from one medium to another, its velocity is doubled. The critical angle for the ray for total internal reflection will be

A) \[30{}^\circ \]

B) \[60{}^\circ \]

C) \[90{}^\circ \]

D) information is incomplete

Correct Answer: A

Solution :

Key Idea: For total internal reflection light travels from denser to rarer medium. Critical angle is the angle of incidence in the denser medium for which the angle of refraction in the rarer medium is \[\text{9}{{\text{0}}^{\text{o}}}.\] From Snells law \[_{2}{{n}_{1}}=\frac{\sin C}{\sin {{90}^{o}}}=\sin C\] Also \[n=\frac{c}{v},\]where c is velocity of light in vacuum and v is velocity in medium. \[\Rightarrow \]               \[\sin C=\frac{{{n}_{1}}}{{{n}_{2}}}=\frac{c/{{v}_{1}}}{c/{{v}_{2}}}=\frac{{{v}_{2}}}{{{v}_{1}}}\] Given,                   \[{{v}_{1}}=2{{v}_{2}}\] \[\therefore \]                  \[\sin C=\frac{1}{2}\] \[\Rightarrow \]                               \[C={{30}^{o}}\]