Thin films: reflection between glass plates

[vetgirl1990]

Homework Statement

Two parallel glass plates of index of refraction n
are separated by an air film of thickness d. Light of wavelength λ
in air, normally incident on the plates, is intensified
on reflection when, for some integer m

a) 2d=mλ
b) 2d=mλ/n
c) 2d=mnλ
d) 2d=(m+1/2)λ
e) 2d=mλ/2

Homework Equations

If only one ray is π shifted: 2nd=mλ (min), 2nd=(m+1/2)λ (max)

If both rays π shifted: 2nd=mλ (max), 2nd=(m+1/2)λ (min)

The Attempt at a Solution

I've attached a diagram of two different for how I picture light should be transmitted in this problem. I'm not sure which one would be a correct approach.

Going with the first diagram,
This would result in a net π shift, so it's conditions would be 2nd=mλ (min) and 2nd=(m+1/2)λ (max).

I chose answer (B) 2d=mλ/n, since the question asks for "intensity increase" so I am assuming it is asking about the condition for a bright fringe; and also because it's one of the only options that takes the index of refraction (n) into account.

I would just like to verify that my reasoning is correct.

 

[ehild]

Homework Statement

Two parallel glass plates of index of refraction n
are separated by an air film of thickness d. Light of wavelength λ
in air, normally incident on the plates, is intensified
on reflection when, for some integer m

a) 2d=mλ
b) 2d=mλ/n
c) 2d=mnλ
d) 2d=(m+1/2)λ
e) 2d=mλ/2

Homework Equations

If only one ray is π shifted: 2nd=mλ (min), 2nd=(m+1/2)λ (max)

If both rays π shifted: 2nd=mλ (max), 2nd=(m+1/2)λ (min)

The Attempt at a Solution

I've attached a diagram of two different for how I picture light should be transmitted in this problem. I'm not sure which one would be a correct approach.

Going with the first diagram,
This would result in a net π shift, so it's conditions would be 2nd=mλ (min) and 2nd=(m+1/2)λ (max).

I chose answer (B) 2d=mλ/n, since the question asks for "intensity increase" so I am assuming it is asking about the condition for a bright fringe; and also because it's one of the only options that takes the index of refraction (n) into account.

I would just like to verify that my reasoning is correct.

You are wrong . The light interference happens because of multiple reflection inside the thin air film between the thick glass plates. d is the thickness of the air film. n is the refractive index of the glass. You can consider the set-up that the air film is surrounded by glass and the light arrives to the glass-air boundary from glass, and reflected from the other side of the air film, from glass.

The