Question

The image of a small electric bulb fixed on the wall of a room is to be obtained on the opposite wall $4m$ away by means of a large convex lens. The maximum possible focal length of the lens required for this purpose will be:
A) $0.5m$
B) $1.0m$
C) $1.5m$
D) $2.0m$

Answer 1

Hint: Recall that the lens is an optical instrument that is made up of two spherical surfaces. If the spherical surfaces are bent outwards, then it is said to be a convex lens. When light rays fall on a convex lens it converges them at a single point. That is why the convex lens is also known as a converging lens.

Complete step by step solution:
Given that the distance between the object (u) and the image (v) is $ = 4m$
Therefore it can be written that
$ \Rightarrow d = u + v$
or $ \Rightarrow d = 4m$
The distance between the focal point and the optical centre of the lens is known as the focal length of the lens.
The maximum focal length of the lens is given by:
$ \Rightarrow {f_{\max }} = \dfrac{d}{4}$
Since the convex lens forms a real image, so focal length can be written as
${f_{\max }} = \dfrac{4}{4}$
$ \Rightarrow {f_{\max }} = 1m$
The maximum focal length required for the image of an electric bulb to be obtained on the opposite side of the wall is $1m$.

Option B is the right answer.

Note: It is important to note that a convex lens is always thicker at the centre and as moved towards the edges it gets thicker. Also since a convex lens converges the light rays, so it always forms either a real or a virtual image of the object. The size of the image formed by a convex lens will be either smaller or larger than that of the object. But in some cases the size of the image is the same as that of the object.