Find Wavelength of Light Wave for Optimal Constructive Interference

[Addez123]

Homework Statement

A wave pass through a 3 layers, at the end they create fully constructive interference, find the wavelength.

Relevant Equations

n1 = 1.5
n2 = 1.29
n3 = 1.42
L = 380 nm

λn = λ/n

The green ray is moved upwards for clarity, they are all on same x-axis with no y component.

Theres a phaseshift at both reflections of the green light because n1 and n3 are > n2.
This results in a complete wavelength phaseshift, aka no impact on the wave.

That means that only the extra travel length has an effect on the phaseshift.
2L = λn
λn = λ/n2 gives us
λ = 2L*n2 = 2 * 380 * 1.29 = 980.4 nm

The correct answer is 490 nm.

What am I doing wrong?

 

[kuruman]

That means that only the extra travel length has an effect on the phaseshift.
2L = λn

Why is it true that 2L = λn?

On edit: What counts is the path length difference between the rays. Also, there is only one reflection of the green ray at the n₁-n₂ interface.

 

[ehild]

λ = 2L*n2 = 2 * 380 * 1.29 = 980.4 nm

The correct answer is 490 nm.

What am I doing wrong?

There is constructive interference when the pathlength -difference is integer times the wavelength. 980 nm is infrared light. Find a visible wavelength.

 

[Addez123]

That was the correct answer, they were looking for visible light.
The equation should've been:
2L = mλ/n
Where m = 1,2,3..
Then the equation turns to λ = 980/m => 490nm