Home
Class 12
PHYSICS
A narrow parallel beam of light is incid...

A narrow parallel beam of light is incident on a transparent sphere of refractives index`n`if the beam finally gets focussed at a point situated at a distance=`2xx("radius of sphere")` form the center of the sphere then find`n`?

Text Solution

Verified by Experts

The correct Answer is:
`4//3`
From first refraction
`(mu_(2))/(v)-(mu_(1))/(u)=(mu_(2)-mu_(1))/(R )`
`(n)/(AI')-(1)/(oo)=(n-1)/(R )`
`AI'=(nR )/(n-1)`
For `2^(nd)` refraction
`u=BI'`
`=AI'-2R`
`=(nR)/(n-1)-2R`
`((n-2n+2)R)/(n-1)`
`u=((2-n))/((n-1))R`
apply`(mu_(2))/(v)-(mu_(1))/(u)=(mu_(2)-mu_(1))/(R )`
`(1)/(R )-(n(n-1))/((2-n)R)`=`(1-n)/(-R )`
`-(n(n-1))/((2-n)R)=(n-1)/(R )-(1)/(R )`
`(n(n-1))/((n-2))=(n-2)`
`n^(2)-n=n^(2)+4-4n`
`3n=4`
`n=4//3`
Promotional Banner

Similar Questions

Explore conceptually related problems

A parallel beam of light falls on a solid tranparent sphere. Q. Which is corret?

A narrow pencil of parallel light is incident normally on a solid transparent sphere of radius r. What should be the refractive index if the pencil is to be focussed (a) at the surface of the sphere, (b) at the centre of the sphere.

A narror parallel beam of light is incident paraxially on a solid transparent sphere of radius r kept in air. What should be the refreative index if the beam is to be focusd (a) at the further surface of the sphere, (b) at the centre of the sphere.

A ray of light is incident on a glass sphere of refractive index 3//2 . What should be the angle of incidence so that the ray which enters the sphere does not comme out of the sphere?

A parallel beam of light is incident on the surface of a transparent hemisphere of radius R and refractive index 2.0 as shown in figure. The position of the image formed by refraction at the first surface is :

A ray of light is incident on a glass sphere of refractive index 3/2. What should be the angle of incidence so that the ray which enters the sphere does not come out of the sphere ?

A ray of light in incident on a glass sphere of refractive index 3//2 . What should be the angle of incidence so that the ray which enters the sphere does not come out of the sphere ?

A parallel beam of light is incident on a lens of focal length 10 cm. A parallel slab of refractive index 1.5 and thickness 3 cm is placed on the other side of the lens. Find the distance of the final image from the lens. .