Question

Focal length of a lens depends on the
(a) Medium constituting lens only.
(b) Medium constituting the surroundings only.
(c) Medium constituting the lens as well as surroundings.
(d) Wavelength of incident light.

• A. only (a)
• B. (a) and (d) both.
• C. (c) and (d) both
• D. only (b)

Answer 1

The correct option is C (c) and (d) both

From lens maker's formula,
$\frac{1}{f}=(\frac{{\mu }_2}{{\mu }_1}-1)(\frac{1}{R_1}-\frac{1}{R_2})$
Where ${\mu }_1$ is refractive index of surrounding and ${\mu }_2$ is refractive index of lens having radius of curvature $R_1$ and $R_2$ respectively.
$\Rightarrow R_1$ and $R_2$ being the radii of curvature are fixed for a given lens.
Also, $\mu =\frac{c}{v}=\frac{c}{f\lambda }$
i.e. $\mu \propto \frac{1}{\lambda }$
Refractive index of a material is inversely proportional to the wavelength of incident light.
$\therefore \left(c\right)$ is correct.
$\begin{array}{c}\text{Why this question}?\\ \text{Tip: For a comprehensive examination of}\\ \text{focal length of a lens, analyse the parameters}\\ \text{involved in lens maker's formula.}\end{array}$