1.

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

Answer»

`R//2n`
`2R//n`
`R//n`
NONE of these

Solution :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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