A hemispherical vessel is completely filled w | vedclass

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

Question

(C) For the coin at $O$ to be visible from point $E$,the light ray must emerge from the liquid surface at the edge $B$. Let $R$ be the radius of the h

Vedclass · Accepted Answer

$\sqrt{2}$

Vedclass · Answer

(C) For the coin at $O$ to be visible from point $E$,the light ray must emerge from the liquid surface at the edge $B$. Let $R$ be the radius of the hemispherical vessel. The ray travels from $O$ to $B$. The angle of incidence $	heta$ at the surface is the angle between the normal at $B$ and the ray $OB$. Since the triangle formed by the center of the top surface,$O$,and $B$ is an isosceles right triangle,the angle $	heta = 45^{\circ}$. For the ray to emerge at the surface,the angle of incidence must be less than or equal to the critical angle $c$. Thus,$	heta \leq c$,which implies $\sin 	heta \leq \sin c$. Since $\sin c = \frac{1}{\mu}$,we have $\sin 45^{\circ} \leq \frac{1}{\mu}$. $\frac{1}{\sqrt{2}} \leq \frac{1}{\mu} \implies \mu \leq \sqrt{2}$. However,for the ray to graze the surface and reach $E$,we require the critical condition $\sin c = \sin 45^{\circ} = \frac{1}{\mu}$. Therefore,$\mu = \sqrt{2}$.

Similar Questions

$A$ point source of light is placed at a depth $h = 0.5 \, m$ below the surface of a liquid $(\mu = \frac{5}{4})$. Then,the fraction of light energy that escapes directly from the liquid surface is:

Light travels in two media $M_{1}$ and $M_{2}$ with speeds $1.5 \times 10^{8} \text{ m/s}$ and $2.0 \times 10^{8} \text{ m/s}$ respectively. The critical angle between them is.

The critical angle for a denser-rarer interface is $45^{\circ}$. The speed of light in the rarer medium is $3 \times 10^8 \, m/s$. The speed of light in the denser medium is:

$A$ ray of light travelling in water is incident on its surface open to air. The angle of incidence is $\theta$,which is less than the critical angle. Then there will be

The phenomenon of total internal reflection is observed when the angle of incidence is

Vedclass Test Series

Exam Paper Generator

Online Exam Module