Question

I need some help understanding the following.

- Light wave interference:
y = m * wavelength (constructive)
y = (m + 0.5) * wavelength (destructive)

- Interference in thin film:
2d = (m + 0.5) * {wavelength in film} (constructive)
2d = m * {wavelength in film} (destructive)

- Clarification:
m : order number
y : distance from center of viewing screen
d : distance between slits

- Question:
I would argue that the constructive interference for the film is still: 2d = m * {wavelength in film} but according to the literature it's: 2d = (m + 0.5) * {wavelength in film} and I cant s