Question

A convex lens is made up of three different materials as shown in the figure. How many images does it form?

Answer 1

Light gets diffracted at different angles for different materials this is due to the fact that different materials have different indexes. Refractive index of a material determines the refractive property of that material. Here to know about the image formation find out the focal length.

Complete step by step solution:
The focal length of a lens and the refractive index is inversely proportional to each other i.e. if the focal length of the material is increased the refractive index of the material decreases the vise-versa is also true. It is given as:
$\dfrac{1}{f} = \left( {\mu - 1} \right)\left( {\dfrac{1}{{{R_1}}} - \dfrac{1}{{{R_2}}}} \right)$ ;
Where:
f = Focal length;
$\mu$= Refractive Index;
R = Radius of Curvature;
The above relation implies that for different refractive index there would be different focal length.
The formation of an image is dependent upon the focal length (shown below) and the focal length is dependent upon the refractive index of the material (shown above).
The relation between the focal length and image formation is dependent upon the three rules of refraction which is given below.
-A ray which is incident and is travelling parallel to the principal axis of converging lens will be refracted through the lens and will be travelling through the focal point which is on the opposite side.
-A ray which is incident and is travelling through the focal point of a convex lens will get refracted and would travel parallel to the principal axis.
-A ray which is incident and is travelling through the centre of the convex lens will continue to go on its path.
From the above given analogy for different refractive indexes there would be different focal points and for different focal points there would be different images and therefore for three different materials with three different refractive indexes there would be three images formed.

A convex lens with three different materials will form three different images.

Note: Here we need to establish a relation between the focal length, refractive index of a material and image formed. First establish the relation between the focal length and the refractive index of a material and then show the relation between the focal length and image formed.