A concave lens is placed in contact with a convex lens of focal length `25 cm`. The combination produces a real image at a distance of `80 cm`, when an object is at a distance of `40 cm`. What is the focal length of concave lens ?

Options

A. `-400 cm`
B. `-200 cm`
C. `+400 cm`
D. `+200 cm`

Answer

A

Explanation

For the combination of lens,
Here, ` u=-40" cm ", v= +80" cm ", f=?`
`therefore" "(1)/(f)=(1)/(80)-(1)/(-40)=(1+2)/(80)=(3)/(80)`
Now, `(1)/(f)=(1)/(f_(1))+(1)/(f_(2))rArr(1)/(f_(2))=(1)/(f)-(1)/(f_(1))`
`(1)/(f_(2))=(3)/(80)-(1)/(25)=(15-16)/(400)=(-1)/(400)rArrf_(2)=-400" cm "`