Three experiments involving a thin film (in air) are shown. If t denotes the film thickness and $\lambda$ denotes the wavelength of the light in the film, which experiments will produce constructive interference as seen by the observer?
A) I only
B) II only
C) III only
D) I and III only
E) II and III only

Question

Three experiments involving a thin film (in air) are shown. If t denotes the film thickness and $\lambda$ denotes the wavelength of the light in the film, which experiments will produce constructive interference as seen by the observer? 
A) I only 
B) II only 
C) III only 
D) I and III only 
E) II and III only

Quizplus · Accepted Answer

In thin film interference, the condition for constructive interference is given by:

2t = mλ/(n_eff)

where 
t = thickness of the film 
m = an integer (1, 2, 3, ...) 
λ = wavelength of light in vacuum 
n_eff = effective refractive index of the film (depends on the refractive indices of the film and the surrounding medium)

Let's analyze each experiment:

Experiment I: The film has a thickness of 1/4λ in air. The light travels through air (n = 1) and then through the film, which has a refractive index greater than 1. Therefore, the effective refractive index is greater than 1.

Thus, for constructive interference, we need:

2t = mλ/(n_eff)

2(1/4λ) = mλ/n_eff

m = 2

Therefore, only the second order maxima (m = 2) will be observed, and the answer is "I only".

Experiment II: The film has a thickness of λ/2 in air. Following the same logic as above, we get:

2t = mλ/(n_eff)

2(λ/2) = mλ/n_eff

m = 2

Therefore, only the second order maxima (m = 2) will be observed, and the answer is "II only".

Experiment III: The film has a thickness of λ/4 in air. The light first travels through air, then through the film, which has a refractive index less than 1. Therefore, the effective refractive index is less than 1.

Thus, for constructive interference, we need:

2t = mλ/(n_eff)

2(λ/4) = mλ/n_eff

m = 2, 4, 6, ...

Therefore, the second, fourth, sixth, etc. order maxima will be observed, and the answer is "I and III only".

Overall, only experiments I and III will produce constructive interference, so the best answer is D.

Three Experiments Involving a Thin Film (In Air) Are Shown λ\lambdaλ

Three Experiments Involving a Thin Film (In Air) Are Shown $\lambda$