Monochromatic light of wavelength, λ is traveling in air. The light then strikes a thin film having an index of refraction n1 that is coating a material having an index of refraction n2. If n2 is larger than n1, what minimum film thickness will result in maximum reflection of this light?

A λ/n1
B λ/2
C λ/(2n1)
D λ/n2
E λ
F λ/4
G λ/(4n2)
H λ/(2n2)
I λ/(4n1)
J The correct response is not shown above.

To find the minimum film thickness that will result in maximum reflection of the monochromatic light, we can use the concept of interference.

When light waves reflect off a thin film, interference occurs between the reflected waves from the top and bottom surfaces of the film. Constructive interference occurs when the path difference between the two waves is equal to an integer multiple of the wavelength λ.

In this case, we want to maximize the reflection, which means we want the reflected waves to interfere constructively. This happens when the path difference is equal to an integer number of wavelengths.

The minimum film thickness that achieves this condition can be determined using the formula:

2t = mλ

Where:
- t is the thickness of the film
- m is an integer representing the order of the interference pattern (for maximum reflection, m = 0)

Now, let's consider the situation. The light is traveling in air and strikes a thin film coated on a material with a higher refractive index (n2 > n1). If n2 > n1, it means that the reflected wave from the top surface experiences a phase change of π (180 degrees) upon reflection, while the reflected wave from the bottom surface experiences no phase change.

When the reflected wave from the top surface undergoes a phase change of π (180 degrees), the path difference between the two waves will be equal to half a wavelength (λ/2). Thus, for maximum reflection, we need the minimum film thickness in such a way that the path difference is equal to half a wavelength.

So, from the formula 2t = mλ, we can solve for the minimum film thickness:

2t = λ/2
t = λ/4

Therefore, the correct response is F) λ/4.