Thin-film interference problem

[NewtonianAlch]

Homework Statement

Light of wavelength 470 nm passes through a block of material with a refractive index n = 1.30, some of it is reflected off the air-block boundary and some of it is transmitted through air (n=1.00) with thickness t, and is then reflected off another block also with n = 1.30.

What is the minimum thickness, t, for which you will observe:

Constructive interference
Destructive intereference

Homework Equations

t = (m+1/2)*lamda / 2n

t = m*lamda / 2n

The Attempt at a Solution

m would be 0 since it's asking for minimum thickness, therefore destructive interference would always be zero wouldn't it?

I'm a bit confused because another book has the equation:

t = (m + 1/2)*lamda / 2 <- what happened to the refraction index?

 

[gneill]

m would be 0 since it's asking for minimum thickness, therefore destructive interference would always be zero wouldn't it?

If t was zero there would be no reflection off the second block, and no interference at all! So you'd not have the setup that the problem specifies.

I'm a bit confused because another book has the equation:

t = (m + 1/2)*lamda / 2 <- what happened to the refraction index?

The refractive index is "bundled" in with the wavelength, lambda; The wavelength used in the equation is the wavelength within the given medium, which depends upon the refractive index.

 

[NewtonianAlch]

If t was zero there would be no reflection off the second block, and no interference at all! So you'd not have the setup that the problem specifies.

Doh! Massive fail.

The refractive index is "bundled" in with the wavelength, lambda; The wavelength used in the equation is the wavelength within the given medium, which depends upon the refractive index.

Ah I see what you mean now.

Thanks a lot!