Answer to Question #87172 in Optics for cookie

Question

Determine:
a) The thinnest soap film (n = 1.33) in air that will result in constructive interference for
reflected light of wavelength 656 nm.
b) What is the next thinnest soap film?
c) Your answers to a) and b) assumed that the rays were normal to the interface. Given
the same film thickness: If you looked at the film from increasing angles of incidence,
would the maximally enhanced wavelength be longer, shorter, or does it stay the same?
Explain very briefly, using a diagram.

Answer 1

(a) Calculate the minimum thickness:

$$t=\frac{(m+\frac{1}{2})\lambda}{2n} (1)$$

where m=0, λ=656 nm, n=1.33

Using the formula (1) we get: t=123.3 nm

(b) What is the next thinnest soap film?

$$t=\frac{(m+\frac{1}{2})\lambda}{2n} (1)$$

where m=1, λ=656 nm, n=1.33

Using the formula (2) we get: t=370.0 nm

(c) Wavelength does not depend on the angle of incidence. If we looked at the film from increasing angles of incidence, would the maximally enhanced wavelength does it stay the same.

Answer:

(a) 123.3 nm

(b) 370.0 nm

(c) wavelength does it stay the same