Question

What happens to the focal length of a convex lens when it is immersed in water? Refractive index of the material of the lens is greater than that of water.

Answer 1

Hint Assume a convex lens having a refractive index n. First, deduce the focal length of the convex lens when it is kept in air, using lens formula. Find the relation between focal length and refractive index of the material. When it is placed in water, using the same relation, explain its effect on focal length.

Complete step by step answer
Let us assume a convex lens of radius of curvature ${R_1}$ at one side and radius of curvature ${R_2}$ on the other side. It is assumed that the convex lens has a focal length $f$. Now, when the lens is on the air medium, there are two mediums to consider. One air as a medium and the glass material as another medium. Using lensmaker’s equation we get,
$\Rightarrow \dfrac{1}{f} = (\mu - 1)[\dfrac{1}{{{R_1}}} - \dfrac{1}{{{R_2}}}]$, where $\mu$is said to be the refractive index of the material with respect to the medium the glass is present in.
When the lens is said to be in air medium,
$\Rightarrow \dfrac{1}{f} = (\dfrac{n}{{{n_{air}}}} - 1)[\dfrac{1}{{{R_1}}} - \dfrac{1}{{{R_2}}}]$
Now, from this equation, wecan deduce a relationship between focal length of the lens and its refractive index n.
$\dfrac{1}{f} \propto (\dfrac{n}{{{n_{air}}}} - 1)$
$\Rightarrow f \propto \dfrac{1}{{(\dfrac{n}{{{n_{air}}}} - 1)}}$
Now, from this relation we can say that, as the refractive index of the medium increases, the focal length of the lens will also increase. Now, it is given in our question that the refractive index in water medium is greater than that of air medium. Thus, since the ${n_{water}}$is greater than air, the overall refractive index is reduced, thus the focal length increases.
Hence, the focal length of the lens increases in water.

Note Refractive index of any material is a dimensionless quantity, which measures the overall bending of light ray, when it passes from one medium to another. In case of greater refractive index of material, the deviation of light rays will be high.