Question

An imaginary line joining the centres of curvature of the two spheres, of which the lens is a part is known as Focal length (f). Is the above statement True or False?
A) True
B) False

Answer 1

Hint: We are given two spheres whose centres of curvature are joined by a line. Now, we know that focal length is the distance between the focus and the centre of a lens and principal axis is a line joining the centres of curvature of the two spheres.

Complete step by step solution:
From the above question we can make a diagram.

Now, from the above diagram we can see that ${C_1}$ and \[{C_2}\] are the centre of the curvature of the two spheres respectively. Now, we know that centre of the distance between the centre of curvatures is known as optical centre, which is represented as $O$ . we also know that focal length is the distance of the centre of curvature to the focus of the lens and principal axis is the line joining the centres of curvatures of the two spheres.

Now, by taking the given options one by one,
Option A: we can see that option A says that the statement given in the problem is true. Now, the statement says that the imaginary line joining the centres of curvature of the two spheres, of which the lens is a part is known as Focal length (f). But, we have discussed above that the line joining the centres of curvature of the two spheres is known as principal axis. Hence, this option is incorrect. Which means that the statement given above is false.

Option B: As we have discussed above that the statement given in the problem is false. So, this is the correct option.

Hence, the correct option is B.

Note: We know that the principal axis is a line passing through the centre of the curvatures of the spheres and through the centre of the surfaces of the spheres. So, principle axis and focal length are the two different quantities.