Waves, Sound, and Physical Optics

A thin film with an index of refraction $n$ and thickness $t$ is on a glass plate with an index of refraction greater than $n$. For a particular wavelength $\lambda$ in air, what is the condition for constructive interference, assuming a phase change at only one boundary?

A thin film of oil ($n = 1.42$) is spread on water. When light of wavelength 500 nm in air is incident normally, strong destructive interference is observed. If the phase change occurs at air-oil interface, what is the minimum thickness of the film?

How does changing the incident angle of light affect the interference pattern observed in thin films?

For destructive interference to occur in thin films, what must be the condition of the interfering waves?

A thin film appears green ($\lambda = 500 \text{ nm}$) at a certain spot. If the refractive index of the film is 1.25, what is the minimum thickness of the film at that spot, assuming constructive interference and one phase change?

When light reflects from a medium with a higher index of refraction compared to the one it's traveling through, what happens to the phase of the reflected light?

Light is incident from air ($n=1$) onto a film of oil ($n=1.45$) on water ($n=1.33$). What is the phase change of the light reflected from the air-oil interface?

A thin film is made of three layers: air ($n=1$), material A ($n=1.5$), and material B ($n=1.3$). Light shines from the air onto material A and then reflects off the interface between material A and material B. What is the net phase change?

What is the primary purpose of antireflection coatings on optical devices?

An antireflection coating is applied to a lens. The coating has a refractive index of $n = 1.38$. What thickness of coating is needed to minimize reflection for light with a wavelength of 550 nm?