A convex lens of focal length 20cm and another plano convex lens of focal length 40cm are placed co-axially . The plano convex lens is silvered on plane surface. What should be the distance (in cm) so that final image of the object 'O' is formed on O itself.

Options

A. 10cm
B. 40cm
C. 20cm
D. 80cm

Answer

c.

Explanation

For plano convex lens`,(1)/(f)=(1)/(40)=((mu-1))/(R)` (i)
For left lens `: (1)/(v_(1))-(1)/(10)=(1)/(20)rArrv_(1)=-20cm`
So image is formed 20cm to left of lens. Distance of image form plano-convex lens is `d+20`. For left surface of plano-convex lens:
`(mu)/(oo)-(1)/(-(d+20))=(mu-1)/(R)rArr (1)/(d+20)=(1)/(40)`
`rArrd=20cm`