Question

An object is placed in front of a symmetrical convex lens with refractive index`1.2`and radius of curvature `40cm`.the surface of the lens further away from the object is silvered.Under auto-collimation condition is ,the obejct distance is
A. `20cm`
B. `10cm`
C. `40cm`
D. `5cm`

Answer 1

Correct Answer - A
`u=2f_(eq)`
`P_(eq)=2P_(1)+P_(m) rArr (1)/(-f_(eq))=(2)/(f_(1))+(1)/(-f_(m))`

`(1)/(f_(1))=((3)/(2)-1)((1)/(40)-(1)/(-40)) rArr(1)/(f_(1))=(1)/(2)xx(1)/(20) rArr (1)/(f_(1))=(1)/(40)`
for mirror
`f_(m)=(R )/(2) rArr f_(m)=(-40)/(2) rArrf_(m)=-20cm`
`(1)/(-f_(eq))=(2)/(f_(1))+(2)/(-f_(m)) rArr (1)/(-f_(eq))=(2)/(40)+(2)/(-20) rArrf_(eq)=-10cm`
`u=R_(eq)=2f_(eq) rArr u=-20cm`