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The image of an object, forme by a plano...

The image of an object, forme by a plano-convex lens at a distance of 8m behind the lens, is real and is one-third the size of the object. The wavelength of light inside the lens is `(2)/(3)` times the wavelength is free space. The radius of the curved surface of the lens is

A

1 m

B

2 m

C

3 m

D

6 m

Text Solution

Verified by Experts

The correct Answer is:
C
Refractive index ` (n) = (lambda_(a))/( lambda_(m)) = (3)/(2)`
Lens maker.s formula
`(1)/(f) = (n - 1) ((1)/(R_(1)) - (1)/(R_(2)))`
`R_(1) = R , R_(2) = - oo`
`rArr (1)/(f) = (0.5)/( R) = (1)/( 2R) rArr f = 2R `
Now, `(1)/(f) = (1)/(v) - (1)/(u)`
[`as m = (v)/(u) rArr (-1)/( 3) = (v)/( u) rArr u = - 3v rArr u = - 24 m` ]
`rArr (1)/( 2R) = (1)/(8) + (1)/(24) rArr R = 3 m `
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