Question

A thin layer of glycerine, index of refraction 1.47, is applied to a sodium chloride crystal, index of

refraction 1.54. A ray of light of wavelength 530 nm travels from air and reflects from the upper and lower surfaces of the thin film. What is the thinnest layer that results in constructive interference between the two reflected rays?

Answer 1

The constructive interference occurs when the path difference (which is double thickness of the film) equals one complete wavelength in the film:

$$2t=\lambda_2.$$

Of course, the wavelength in the film is not the original wavelength $\lambda$:

$$\lambda_2=\frac{\lambda}{n_2}.$$

Therefore:

$$t=\frac{\lambda_2}{2}=\frac{\lambda}{2n_2}=\frac{530}{2\cdot1.47}=180\text{ nm}.$$