Question

Focal length of a convex lens will be maximum for

• A. blue light
• B. green light
• C. yellow light
• D. red light

Answer 1

The correct option is D

red light

The explanation for the correct option

Option D: red light

1. The relation between the focal length, refractive index, and radius of curvature is given as
   $\frac{1}{f}=(\mu -1)(\frac{1}{R_1}-\frac{1}{R_2})$
   Where $f$is the focal length of the lens, $\mu$ is the refractive index of the color of light in the medium, $R_1$ is the radius of curvature of surface 1 and $R_2$ is the radius of curvature of surface 2.
2. In the visible spectrum, the colors of light are in the sequence of VIBGYOR.
3. The wavelength increases from violet color to red color, but considering Cauchy's formulae $\mu =\frac{A}{\lambda }+\frac{B}{{\lambda }^2}+\frac{C}{{\lambda }^4}........$ , refractive index $\mu$ decreases as the wavelength $\lambda$ increases.
4. So the refractive index will vary as ${\mu }_V>{\mu }_I>{\mu }_B>{\mu }_G>{\mu }_Y>{\mu }_O>{\mu }_R$.
5. According to the relation, focal length and refractive index are inversely proportional to each other.
6. The larger the refractive index of the given colour, the lower will be the focal length.
7. The variation of focal length will be given as $f_R>f_O>f_Y>f_G>f_B>f_I>f_V$.

Thus, the focal length of a convex lens will be maximum for red color.

Hence, option (D) is correct.