A point source of light S is placed at the bo | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) For the source $S$ to be invisible from above,the light rays from $S$ must undergo total internal reflection at the liquid-air interface or be blo

Vedclass · Accepted Answer

$1.33$

Vedclass · Answer

(C) For the source $S$ to be invisible from above,the light rays from $S$ must undergo total internal reflection at the liquid-air interface or be blocked by the opaque disc $D$. The condition for the source to be completely hidden is that the radius of the disc $r$ must be at least equal to the radius of the circle of illumination formed by the critical angle $	heta_c$ at the surface.The radius $r$ of the circle of illumination is given by:$r = h 	an 	heta_c$Since $\sin 	heta_c = 1/\mu$,we have $	an 	heta_c = \frac{1}{\sqrt{\mu^2 - 1}}$.Thus,$r = \frac{h}{\sqrt{\mu^2 - 1}}$.Given $r = 1\, cm$ and $\mu = 5/3$,we substitute these values:$1 = \frac{h}{\sqrt{(5/3)^2 - 1}}$$1 = \frac{h}{\sqrt{25/9 - 1}}$$1 = \frac{h}{\sqrt{16/9}}$$1 = \frac{h}{4/3}$$h = 4/3 = 1.33\, cm$.Therefore,the maximum height of the liquid is $1.33\, cm$.

Similar Questions

$A$ wide container is filled with water $\left(\mu=\frac{4}{3}\right)$ up to a height of $1 \ m$. Find the diameter of the disc at the top of the water surface from which light is coming out.

Which of the following is used in optical fibres?

In the figure,the optical fiber is $L = 2\,m$ long and has a diameter of $d = 20\,\mu m$. If a ray of light is incident on one end of the fiber at an angle $\theta_1 = 40^\circ$,the number of reflections it makes before emerging from the other end is close to:

The reason for the shining of an air bubble in water is

Vedclass Test Series

Exam Paper Generator

Online Exam Module