Physics Question on Ray optics and optical instruments

Question

Focal length of a convex lens will be maximum for

Answer 1

Solution

The focal length of a convex lens depends on the refractive index of the material it is made of, as well as the wavelength of light passing through it. The refractive index of a material varies slightly with different wavelengths of light, causing the focal length to change.
In general, the refractive index of a material decreases as the wavelength of light increases. This phenomenon is known as dispersion. Since red light has the longest wavelength among the options given (red light has a longer wavelength than green, blue, and yellow light), the refractive index of the lens material will be the least for red light.
According to the lens maker's formula, a lower refractive index corresponds to a longer focal length for a convex lens. Therefore, the focal length of a convex lens will be maximum for (C) red light.