Question

The walls of a soap bubble have about the same index of refraction as that of plain water, n=1.33, There is air both inside and outside the bubble. 

( a) What wavelength ( in air) of visible light is most strongly reflected from a point on a soap bubble where its wall is 290 nm thick? To what color does this correspond?

( b) Repeat part ( a) for a wall thickness of 340 nm.

Answer 1

Concepts and reason

The concept used to solve this problem is based on wavelength.

Initially, the value of the wavelength of visible light can be calculated by using the relationship between wavelength, thickness, and refractive index. Later, the value of the wavelength of visible light can be calculated by using the relationship between wavelength, thickness, and refractive index.

Fundamentals

The expression for the wavelength in terms of thickness and refractive index is given below:

Here, is the thickness of the soap bubble, is the refractive index of water, is the integer, andis the wavelength of light.

The range of visible light is.

(a.1)

The expression for wavelength is given below:

Substitute for, for and for and rearrange to find .

(a.2)

The expression for the wavelength is given below:

Substitute for, for and for and rearrange to find .

(a.3)

The expression for the wavelength is given below:

Substitute for, for and for and rearrange to find .

Therefore, from section a.1, a.2, a.3, the wavelength of the visible light strongly reflected from the soap bubble is .

(b.1)

The expression for the wavelength is as follows:

Substitute for, for and for and rearrange to find .

(b.2)

The expression for the wavelength is given below:

Substitute for, for and for and rearrange to find .

(b.3)

The expression for the wavelength is given below:

Substitute for, for and for and rearrange to find .

Therefore, from sections b.1, b.2, b.3, the wavelength of the visible light strongly reflected from the soap bubble is .

Ans: Part a

The wavelength of the visible light, which is strongly reflected, is.

Part b

The wavelength of the visible light, which is strongly reflected, is.