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JEE Mains · Physics · STD 12 - Ray optics and optical instruments
- JEE Mains 2013
- Hard
- MCQ
Light is incident from a medium into air at two possible angles of incidence \((A)\, 20^o\) and \((B)\, 40^o\) . In the medium light travels \(3.0\, cm\) in \(0.2\, ns\). The ray will
Pick an option to check your answer.
Answer & Solution
Correct Answer
(B) suffer total internal reflection in case \((B)\) only
Step-by-step Solution
Detailed explanation
Velocity of light in medium
\({V_{{\text{treat }}}} = \frac{{3\,{\text{cm}}}}{{0.2\,{\text{ns}}}} = \) \(\frac{{3 \times {{10}^{ - 2}}{\text{m}}}}{{0.2 \times {{10}^{ - 9}}{\text{s}}}} = 1.5\,{\text{m}}/{\text{s}}\)
Refractive index of the medium
\(\mu = \frac{{{V_{{\text{air }}}}}}{{{V_{{\text{med }}}}}} = \) \({\frac{{3 \times {{10}^8}}}{{1.5}} = 2\,{\text{m}}/{\text{s}}}\)
As \(\mu=\frac{1}{\sin C}\)
\(\therefore \sin C=\frac{1}{\mu}=\frac{1}{2}=30^o\)
Condition of \(TIR\) is angle of incidence i must be greater than critical angle. Hence ray will suffer \(TIR\) in case of \((B)\) \(\left(i=40^o > 30^o \right)\) only.
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