Question

A convex lens of power P is immersed in water. How will its power change?
A) Increases
B) Remains Unchanged
C) Decreases
D) Increases for red colour and decreases for blue colour

Answer 1

In order to find the correct answer to this question, it is important to be very well aware of the mathematical relationship between the power of a convex lens and the change in refractive index. We can use this mathematical equation to find how the power of the convex lens will change when it is immersed in water.

Complete step by step answer:
We know that the relationship between the power of a convex lens and the refractive index of the surroundings is given by the mathematical expression given below:
$P = \dfrac{1}{f} = ({n_2} - {n_1})\left[ {\dfrac{1}{{{R_1}}} - \dfrac{1}{{{R_2}}}} \right]$

Now, in this mathematical formula for power of a convex lens, the physical quantity ${n_1}$ is the refractive index of the medium in which the lens is placed and ${n_2}$ is the refractive index of air.

Now, we know that the value of the refractive index of water is equal to $1.33$ and the refractive index of air is equal to unity thus, ${n_2} = 1$. Thus, we get that ${n_2} = 1$ and ${n_1} = 1.33$. Thus, we see that the value of the refractive index of the medium in which the lens is placed is more than that of the refractive index of air. This is because the refractive index of water is more than the refractive index of air.
Now, as ${n_2} > {n_1}$. We can say the power of the convex lens will decrease for this reason.

Note: We see that the value of the focal length of the convex lens increases and as a result of which the power decreases. This is because power of a convex lens is inversely proportional to the focal length of the convex lens.