Two convex lenses, each of focal length 10 cm, are places at a separation of 15 cm with their principal axes coinciding. (a) Show that a light beam coming parallel to the principal axis diverges as it comes out of the lens system. (b) Find the location of the virtual image formed by the lens system of an object placed far away. (c) Find the focal length of the equivalent lens. (note that the sign of the focal length is positive although the lens system actually diverges a parallel beam incident on it.)

focal length of both the lens, = 10cm

Distance between both the lens, d = 15cm

(a) lights will fall parallel to the principle axis of the lens; therefore, rays will converge at the focus of the second lens. Hence all the rays emerging from the system will be diverging, as shown in the figure

(b) using lens formula, for first lens,

For the second convex lens,

The distance of source and the lens, u= (15-10) = -5cm

Let = object distance from the second convex lens, then

using lens formula,

Thus, the virtual image will be formed at 5cm from first lens.

(c) The equivalent focal length of the lens system, F is given by

As we know, both the focal lengths are same, i.e. 10cm