Q1: Two concave lenses of 60 cm focal length are cemented on either side of a convex lens of 15 cm focal length. The focal length of the combination is

ANS:C - 30 cm

Concave (-) and convex (+).

Given:
Two concave i.e F1 = -1/60.
F2 = -1/60.

One convex lens i.e F3 = 1/15.
combined focal length = (F1 + F2) + F3.
= { ( -1/60) + ( -1/60) } + 1/15,
= (-2/60) + 1/15,
= -1/30 + 1/15,
= -1+2/30,
= 1/30 = 30. Formula: 1/f = 1/f1 + 1/f2.

According to the problem 60 cm on the either side i.e. f1 = f2 = 60 & focal length combination f = ?
Now, 1/f = 1/f1 + 1/f2.
1/f = 1/60 + 1/60.
= 1/30. So combination is 30. We know that the focal length of the concave lens is negative and convex lens is positive then the focal length of the combination can be found out by using lens formula. Convex is magnifying glass, makes image larger. So its behavior is making big +ve. Concave is indicated as -ve.

Now three lenses are combined to make single lens. To get the property of new lens we have to find out its focal length, it can be calculated by 1/f = 1/f1+1/f2+1/f3.

f1 = f2 = 60, f3 = 15. You will get f = 30.