Question

White light is incident from under-water on the water-air interface. If the angle of incidence is slowly increased from zero, the emergent beam coming out into the air will eventually turn into

[Assume, reflection at interface is negligible]

• A. violet
• B. red
• C. black
• D. green

Answer 1

The correct option is C black

We know that,

For a water-air interface,

$\sin {\theta }_c=\frac{{\mu }_{air}}{{\mu }_{water}}$

$\Rightarrow \sin {\theta }_c=\frac{1}{{\mu }_{water}}$

$\Rightarrow \sin {\theta }_c=\frac{\lambda }{{\lambda }_0}$ $[\because {\mu }_{water}=\frac{c}{v}=\frac{{\lambda }_0}{\lambda }]$

So, ${\theta }_c\propto \lambda$

For all angles less than ${90}^{\circ }$ , $\sin \theta$ increases as $\theta$ increases.

In $\text{VIBGYOR}$, wavelength $\lambda$ varies from $400\text{nm}$ to $700\text{nm}$.

So, for violet $\lambda$ is minimum and for red it is maximum.

When angle of incidence is zero all colours of light emerge out of water, as a white light. With increase in angle of incidence , first violet gets total internally reflected, then all other colours get total internally reflected with increase in incident angle.

Hence, the emergent ray will vanish after every wavelength of visible light gets total internally reflected.

Hence, option (c) is the correct answer.

Why this question? Note:- At an interface, critical angle varies with wavelength of incident light.