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

For constructive interference in thin films, the path difference between the reflected waves from the top and bottom surfaces of the film must be an integer multiple of the wavelength in the film. Thus, we have:

Experiment I: 
Path difference = 2t
Constructive interference occurs when 2t = m1λ1, where m1 is an integer
Thus, constructive interference can occur for various values of t and λ1

Experiment II: 
Path difference = 2t + λ1/2
Constructive interference occurs when 2t + λ1/2 = m1λ1, where m1 is an integer
This condition cannot be satisfied as λ1/2 is always smaller than λ1, therefore, there will be destructive interference.

Experiment III: 
Path difference = 2t + λ1
Constructive interference occurs when 2t + λ1 = m1λ1, where m1 is an integer
Thus, constructive interference can occur when t = (m1/2 - 1/4)λ1

Therefore, only experiments I and III can produce constructive interference.

Three Experiments Involving a Thin Film (In Air)are Shown λ\lambdaλ Denotes the Wavelength of the Light in the Film, Which

Three Experiments Involving a Thin Film (In Air)are Shown $\lambda$ Denotes the Wavelength of the Light in the Film, Which