Question

A converging lens of focal length 20cm is made up of a material of refracting index is 1.1 and is immersed in water. The lens will behave as a:
A) Convergent lens of focal length 20cm
B) Convergent lens of focal length lesser than 20cm
C) Divergent lens
D) Plane glass plate

Answer 1

The behaviour of a lens is to be found by comparing the refractive indices of the material of the lens and the medium in which the lens is kept. The lens maker's formula can be used to find out whether the lens behaves oddly in a given medium.

Complete answer:
Let us consider the situation in which a lens of refractive index 1.1 is kept in water which has a refractive index of 1.33. Let use apply the Lens makers formula as –

& \dfrac{1}{f}=({{\mu }_{21}}-1)(\dfrac{1}{{{R}_{1}}}-\dfrac{1}{{{R}_{2}}}) \\\ & f=+20cm \\\ & \\\ \end{aligned}$$ Where, f is the focal length of the lens depending on the media 1 and 2. When the medium 1 is air the focal length is $$+20cm$$and is therefore, converging in nature Now, let the medium 1 be water and the medium be the material of the lens. The lens makers formula will give as – $$\begin{aligned} & \dfrac{1}{f'}=(\dfrac{1.1}{1.33}-1)(\dfrac{1}{{{R}_{1}}}-\dfrac{1}{{{R}_{2}}}) \\\ & \dfrac{1.1}{1.33}-1=-ve \\\ & \Rightarrow \dfrac{1}{f'}<0 \\\ & \text{and,} \\\ & \therefore \text{ }f'<0 \\\ \end{aligned}$$ When the focal length is negative it implies that the lens diverges the light falling on it. Therefore, the lens is diverging when in water. **The correct answer is option C.** **Note:** The terminology for convex lenses as the converging lenses is given on the fact that it converges the light beam when it is kept in a usual medium, i.e., the air. We should not be confused with this usage for other media like water which has a higher refractive index.