An object is placed at a distance of 10cm form a co-axial combination of two lenses A and B in contact. The combination forms a real image three times the size of the object. If lens B is concave with a focal length of 30cm. The nature and focal length of lens A is

Options

A. convex,12cm
B. concave,12cm
C. convex,6cm
D. convex,18cm

Answer

C

Explanation

`therefore` Magnification, `m=(v)/(-u)=-3`
v=3u=30cm
Focal length of co-axial combination.
`(1)/(f_(1))+(1)/(f_(2))=(1)/(v)-(1)/(u)`
`-(1)/(30)+(1)/(f_(2))=(1)/(30)+(1)/(10)+(4)/(30)`
`(1)/(f_(2))=(4)/(30)+(1)/(30)`
`(1)/(f_(2))=(4+1)/(30)+(5)/(30)`
`f_(2)=(30)/(5)=6cm`
Hence, lens is convex lens.