Two thin lenses of powers 2D and 4D are placed in close contact. An object is placed at a distance of 50 cm from the combination. What is the distance of the image from the combined lens ?

Options

A. 30 cm
B. 40 cm
C. 25 cm
D. 35 cm

Answer

C

Explanation

The combined focal length of the lens is given by
`(1)/(F) =(1)/(f_(1))+(1)/(f_(2)) because (1)/(f)=P`
`therefore P=P_(1)+P_(2)=2+4=6D`
`therefore 6=(100)/(F) therefore F=(100)/(6)=(50)/(3) cm`
The combined lens acts as a convex lens.
For this lens, `(1)/(v)-(1)/(u)=(1)/(F)`
`therefore (1)/(v) =(1)/(F) +(1)/(u)" but " u=-50 cm`
`therefore (1)/(v)=(3)/(50)-(1)/(50)=(2)/(50)=(1)/(25)`
` therefore v=25 cm` (real image)