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A point object is placed in front of a s...

A point object is placed in front of a silvered plano convex lens of refractive index `n` radius of curvature `R`, so that its image is formed on itself. Then the object distance is equal to

A

`R//2n`

B

`2R//n`

C

`R//n`

D

none of these

Text Solution

Verified by Experts

The focal length of the combination is given as
`(1)/(f)=(1)/(f_(t))+(1)/(f_(l))+(1)/(f_(m))`
where `f_(m)=R//2` & `(1)/(f_(l))=(n-1)((1)/(oo)-(1)/(-R ))=(n-1)/(R )`
`rArr (1)/(f)=(2(n-1))/(R )+(2)/(R )=(2n)/(R )rArr f=(R )/(2n)`
`rArr 2f=(R )/(n)`
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