A convex and a concave lens separated by distance d are then put in contact . The focal length of the combination

Options

A. becomes 0
B. remains the same
C. decreases
D. increases

Answer

A

Explanation

Focal length of a combination is
`(1)/(F)=(1)/(f_(1))+(1)/(f_(2))-(d)/(f_(1)f_(2))`.
As `f_(2)` is negative , `(1)/(F_(1))=(1)/(f_(1))-(1)/(f_(2))+(d)/(f_(1)f_(2))`

When put together , `(1)/(F_(2))=(1)/(f_(1))-(1)/(f_(2))`
`thereforeF_(1)=(f_(1)f_(2))/(f_(2)-f_(1)+d),F_(2)=(f_(1)f_(2))/(f_(2)-f_(1))`.
Therefore the focal length for this combination , become larger If `f_(1)=f_(2)`, this combination gives infinity contact and not zero . Therefore for the option given differnt focal lengths are assumed.