A point object is placed at a distance of 15 cm from a convex lens. The image is formed on the other side at a distance of 30 cm from the lens. When a concave lens is placed in contact with the convex lens, the image shifts away further by 30 cm. Calculate the focal lengths of the two lenses.

Answer

A, C, D

Explanation

Let u = object distance from convex lens =-15 cm `usilon_1` = image distance from convex lens = 30 cm `f_1` = forcal length of convex lens
`Now, (1)/(upsilon_1) - (1)/((u))= (1)/(f_1)`
or ` (1)/(f_1) = (1)/(30) - (1)/((-15)) = (1)/(30) +(1)/(15)`
`or f_1 = (30xx 15)/(30 +15) = (450)/(45)`
=10 cm
Again, let `upsilon` = image (final) distance from concave lens = + (30 + 30) = + 60 cm
`upsilon_1` = object distance from concave lens = +30 cm
`f_2` = focal length of concave lens
Now, `(1)/(upsilon) -(1)/(upsilon_1) = (1)/(f_1)`
or `(1)/(f_1) = (1)/(60) - (1)/(30)`
`=(30-60)/(60xx 30) = (-30)/(60xx30)`
or `f_2 = -60 cm`
So, the focal length of convex lens is 10 cm and that of concave is 60 cm.