Question

The focal length of a lens is $10cm$ when kept in air. Now if we keep the lens into the water, the focal length ___________.

• A. will be equal to 10 cm.
• B. will be greater than 10 cm
• C. will be lesser than 10 cm
• D. cannot be predicted

Answer 1

The correct option is B will be greater than 10 cm

According to lens maker formula,
$\frac{\text{1}}{\text{f}}$ =$\text{(n-1)(}$$\frac{\text{1}}{R_1}$-$\frac{\text{1}}{R_2}$$\text{)}$
Where, $f$ is the focal length of the lens in the medium where it is kept.
$n$ is the refractive index of the lens with respect to the medium.
$R_1$ and $R_2$ are the radii of curvature of the lens's first and second refracting surface respectively.
$R_1$ and $R_2$ will remain unchanged even if we change the medium from air to water. We know that refractive index of lens with respect to water is lesser than the refractive index of lens with respect to air.
i.e, $n_{lw}$ < $n_{la}$
$⟹$ $f_{water}$ > $f_{air}$ (From the lens maker formula)
Therefore, when we keep the lens in water, its focal length will increase.