Question

Consider convex lens made of material with refractive index $\mu$ depending of wavelength as $\mu = a + \frac{b}{\lambda^2}$, where a & b are constants.

• A. Focal length of lens for violet colour will be equal to that of red colour.
• B. Focal length for yellow colour will be higher to that of orange colour
• C. Focal length for orange colour will be higher to that of yellow colour
• D. Focal length for colour will be of order $f_{orange} > f_{green} > f_{red}$.

Answer 1

Answer: (C)

C. Focal length for orange colour will be higher to that of yellow colour

Answer 2

The refractive index is given by $\mu = a + \frac{b}{\lambda^2}$. Assuming $b > 0$, $\mu$ decreases as $\lambda$ increases. From the lens maker's formula, $\frac{1}{f} = (\mu - 1)K$, so $f = \frac{1}{(\mu - 1)K}$. As $\mu$ decreases, $f$ increases. The order of wavelengths is Violet < Yellow < Orange < Red. Thus, the focal lengths follow the order $f_{violet} < f_{yellow} < f_{orange} < f_{red}$. Therefore, $f_{orange} > f_{yellow}$.