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, 12 cm
B. Concave, 12 cm
C. Convex, 6cm
D. Convex , 18 cm

Answer

C

Explanation

u = - 10 cm, m = -3
m = `(v)/(u) rArr - 3 = (v)/(-10) rArr v = 30` cm
`(1)/(f_(eq)) = (1)/(v) + (1)/(u) = (1)/(30) + (1)/(10) = (1+ 3)/(30) rArr f_(eq) = (30)/(4) = 7.5` cm
Now, `(1)/(f_(eq)) = (1)/(f_(1)) + (1)/(f_(2))`
`rArr (4)/(30) = -(1)/(30) + (1)/(f_(2)) rArr (1)/(f_(2)) = (5)/(30) rArr f_(2) = 6 `cm
Convex in nature.