A concave lens forms the image of an object such that the distance between the object and image is `10 cm` and the magnification produced is `1//4`. The focal length of the lens will be

Options

A. `-6.2` cm
B. `-4.4` cm
C. `-8.6` cm
D. `-10` cm

Answer

B

Explanation

A concave lens forms virtual image I of a point object O.
As, `m=(1)/(4)=(v)/(u):.u=4v`
If `v=-x, u=-4x`
Distance between object and image,
`|OI|=4x-x=3x=10` cm,
or `x=(10)/(3)` cm
`:.u=-(40)/(3)` cm and `v=(-10)/(3)` cm
Using lens formula, `(1)/(f)=(1)/(v)=(1)/(u)`
`(1)/(f)=-(3)/(10)+(3)/(40)=-(9)/(40), :.f=-(40)/(9)` cm= `-4.4` cm