A biconvex thin lens is prepared from glass of refractive index `3//2.` The two bounding surfaces have equal radii of `25cm` each. One of the surfaces is silvered from outside to make it reflecting. Where should an object be placed before this lens so that the image coincides with the object.

Explanation

Here ` R_1 = + 25 cm R_2 =- 25 cm , and mu= 3//2`
image coincides with object ,
hence ` u= v=-x ` (say )
`(1)/(F ) =(2)/(F_L) +(1)/(F_C ) =2 (3/2 -1) (2)/( 25 ) + (2)/(25 ) implies (1)/(F ) = (4)/( 25)`
By using ` (1)/( v ) - (1)/( u ) = (1)/(f) `
` implies - (1)/(x) - (1)/(x ) = (4)/(25 )`
` x= 12.5 cm`
Hence, the object should be placed at a distance 12.5 cm in front of the silvered lens.