Question

Focal length of a lens for red colour is:
(A) Same as that for violet.
(B) Greater than that violet.
(C) Lesser than that for violet.
(D) None of the above

Answer 1

Hint: It is essential to know that for different wavelengths of light, the focal point or the point of convergence of light rays, varies for different colors of light and hence the lens depends on the color of light. We can use lens formulas to understand further.

Complete step by step answer:
White light, when passed through a glass prism or lens has a tendency to split itself into seven colors namely violet, indigo, blue, green, yellow, orange and red. This occurs when a white light passes through a prism of varied refractive index. According to layman terms, the refractive index is defined as the ratio of speed of light to the phase velocity of light in the secondary medium.
Refractive index is one of the factors by which the speed of light in the second medium is reduced and at the same time, which affects the wavelength of the radiation. Wavelength in the second medium can be given as the ratio of wavelength in the first medium and the refractive index of the glass. Now since, red is the last color that gets split, it reaches a greater length and will have a greater wavelength. Since the wavelength is greater than violet, its focal length relation can be determined using lens formula
Lens formula is given as\[\dfrac{1}{f} = (\mu - 1)(\dfrac{1}{{{R_1}}} - \dfrac{1}{{{R_2}}})\], where \[\mu \]is the refractive index of the material. Now, refractive index is inversely proportional to the wavelength of light in the medium and is also inversely proportional to the focal length. Since, red has greater wavelength, it has greater focal length than violet.

Hence, option (b) is the right answer.

Note: Newton’s circular disc is a phenomenon where a circular disc painted with all seven colors , will be turned rapidly, producing back white light. This is also called temporal optical mixing that undergoes the additive and averaging process of color mixing.