Question

A soap bubble is 95 nm thick and illuminated by white light incident perpendicular to its surface.

The longest wavelength in nm which is constructively reflected, assuming soap has the same index of refraction as water (n = 1.33) is equal to 505.4 nm.

Draw a diagram of the mediums showing where, if any, a phase change occurs.

State whether you are looking for constructive of destructive interference.

Answer 1

Consider two light rays that are reflected as shown below.

The first ray enters the water and is reflected in the interface where the second medium has a lesser refractive index than the first. So, there will be no phase change.

For the second light ray that gets reflected from the top surface, the reflection occur at a lower refractive index than the second medium. So, there is a phase change of (the reflected wave is inverted)

Here, the light rays are entering at an angle of 90 degrees.

For the second ray, there is a phase change of . This equals to a path change of .

For the first ray, there is a path difference, because it has to travel an extra distance of 2d

The wavelength of light inside the medium is given by

Where n₁ is the refractive index of air and n₂ is the refractive index of water.

The initial wavelength is 505.4 nm

Here, d = 95 mn

So, 2d = 190 nm

The path change occuring is equal to 190/380 = 1/2 =

For both the top and bottom reflected light, the path change is the same. So, the interference will be constructive.