Optics 2 Question 4
4. A green light is incident from the water to the air-water interface at the critical angle $(\theta)$. Select the correct statement.
(2014 Main)
(a) The entire spectrum of visible light will come out of the water at an angle of $90^{\circ}$ to the normal
(b) The spectrum of visible light whose frequency is less than that of green light will come out of the air medium
(c) The spectrum of visible light whose frequency is more than that of green light will come out to the air medium
(d) The entire spectrum of visible light will come out of the water at various angles to the normal
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Answer:
Correct Answer: 4. (d)
Solution:
- For total internal reflection of light take place, following conditions must be obeyed.
(i) The ray must travel from denser to rarer medium.
(ii) Angle of incidence $(\theta)$ must be greater than or equal to critical angle $(C)$
$$ \text { i.e. } \quad C=\sin ^{-1} \frac{\mu _{\text {rarer }}}{\mu _{\text {denser }}} $$
Here, $\sin C=\frac{1}{n _{\text {water }}}$ and $n _{\text {water }}=a+\frac{b}{\lambda^{2}}$
If frequency is less $\Rightarrow \lambda$ is greater and hence, RI $n _{\text {(water) }}$ is less and therefore, critical angle increases. So, they do not suffer reflection and come out at angle less than $90^{\circ}$.
