Focal length of the plano-convex lens is 15 cm. A small object is placed at A as shown in the figure. The plane surface is silvered. The image will form at `

Options

A. 60 cm left of lens
B. 12 cm left of lens
C. 60 cm right of lens
D. 30 cm left of lens.

Answer

B

Explanation

When thin lenses in contact are finally terminated by a mirror then combination acts like a mirror whose focal length can be given by the following formula :
`(1)/(F)=-2((1)/(f_(1))+(1)/(f_(2))+….)+(1)/(f_(m))`
Here in this case there is only one lens of focal length `15cm(f_(1)=15cm)` and there is planar mirror at the end hence `f_(m)=oo`.
`(1)/(F)=-2((1)/(15))+(1)/(oo)`
`rArr" "F=-7.5cm`
Hence this given system is same as concave mirror of focal length 7.5 cm.
For mirror we can write the following equation :
`(1)/(F)=(1)/(v)+(1)/(u)`
`rArr" "(1)/(-7.5)=(1)/(v)+(1)/(-20)`
`rArr" "(1)/(v)=(1)/(20)-(2)/(15)`
`rArr" "(1)/(v)=(3-8)/(60)=(-5)/(60)`
`rArr" "v=-12cm`
Hence 12 cm to the left of lens.
Hence option (b) is correct.