A parallel beam of light emerges from the opp | vedclass

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

Question

(C) Let the radius of the sphere be $R$. The point source is at $O$ on the surface of the sphere. The light rays travel through the sphere and emerge

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(C) Let the radius of the sphere be $R$. The point source is at $O$ on the surface of the sphere. The light rays travel through the sphere and emerge from the opposite surface at $P$ as a parallel beam.Applying the refraction formula at the spherical surface: $\frac{\mu_2}{v} - \frac{\mu_1}{u} = \frac{\mu_2 - \mu_1}{R}$.Here,the light travels from the sphere (refractive index $\mu$) to the air (refractive index $1$).Thus,$\mu_1 = \mu$,$\mu_2 = 1$.The object distance $u$ from the surface $P$ is the diameter of the sphere,so $u = -2R$.The image is formed at infinity,so $v = \infty$.The radius of curvature of the surface at $P$ is $R$,but since the center of curvature is to the left of $P$,the radius is taken as $-R$.Substituting these values: $\frac{1}{\infty} - \frac{\mu}{-2R} = \frac{1 - \mu}{-R}$.$0 + \frac{\mu}{2R} = \frac{\mu - 1}{R}$.$\frac{\mu}{2} = \mu - 1$.$1 = \mu - \frac{\mu}{2} = \frac{\mu}{2}$.$\mu = 2$.

$A$ parallel beam of light emerges from the opposite surface of the sphere when a point source of light lies at the surface of the sphere. The refractive index of the sphere is

Similar Questions

$A$ point object is placed at the centre of a glass sphere of radius $6 \, cm$ and refractive index $1.5$. The distance of the virtual image from the surface of the sphere is.....$cm$

$A$ concave spherical surface of radius of curvature $10 \ cm$ separates two media $X$ and $Y$ of refractive index $4/3$ and $3/2$ respectively. If the object is placed along the principal axis in medium $X$,then:

In a thin spherical fish bowl of radius $10 \, cm$ filled with water of refractive index $\mu = \frac{4}{3}$,there is a small fish at a distance of $4 \, cm$ from the center as shown in the figure. Where will the image of the fish appear if seen from point $F$ (in $, cm$)?

$A$ spherical vessel of radius $10 \, cm$ is filled with water of refractive index $\mu = 4/3$. $A$ fish is at a distance of $4 \, cm$ from the center as shown in the figure. If viewed from end $E$,at what distance will the fish appear to be (in $, cm$)? (Neglect the thickness of the vessel)

Vedclass Test Series

Exam Paper Generator

Online Exam Module