Question

Focal length of a lens for red colour is

• A. same as that for violet
• B. greater than that for violet
• C. lesser than that for violet
• D. none of the above

Answer 1

The correct option is B greater than that for violet

From lensmaker's formula, we have $\frac{1}{f_{\text{lens}}}=(\mu -1)K_{\text{lens}}$

Thus, as $\mu$ increases, the focal length $f$ decreases.

We know that the relation between wavelength and refractive index is given by $\mu \left(\lambda \right)=A+\frac{B}{{\lambda }^2}$

Thus, as $\lambda$ increases, the refractive index $\mu$ decreases

We know that in the visible spectrum, the increasing order of wavelengths is given by VIBGYOR.

Thus, ${\lambda }_{\text{red}}>{\lambda }_{\text{violet}}\Rightarrow {\mu }_{\text{red}}<{\mu }_{\text{violet}}\Rightarrow f_{\text{red}}>f_{\text{violet}}$