A glass (n = 1.6)lens is coated with a thin film (n = 1.3)to reduce reflection of certain incident light.If$\lambda$ is the wavelength of the light in the film, the least film thickness is:

Question

Quizplus · Accepted Answer

To reduce reflection of certain incident light, the thin film must be of such thickness that the light reflected from the top surface and the bottom surface of the film combines destructively. This means that the path difference between the two reflected beams should be λ/2, where λ is the wavelength in the film.

Let t be the thickness of the film. Then, using the formula for the optical path difference due to a medium of refractive index n,
2nt = (m+1/2)λ

where m is an integer. Since the film is thin, we can take m = 0. Also, the wavelength of the light in the glass is given by λ/n, where n is the refractive index of the glass. Therefore, we have
2nt/n = λ/2
or t = λ/4n

Substituting the given values, we get
t = F1F1F1S1F1F1F10/4

Therefore, the least film thickness is F1F1F1S1F1F1F10/4. Answer choice B is correct.

A Glass (N = 1 λ\lambdaλ Is the Wavelength of the Light in the Film, the Film

A Glass (N = 1 $\lambda$ Is the Wavelength of the Light in the Film, the Film