Question

A soap bubble is essentially a thin film of water surrounded by air. The colors you see in soap bubbles are produced by interference. What visible wavelengths of light are strongly reflected from a 390 nm-thick soap bubble? What color would a 390 nm-thick soap bubble appear to be (green, purple, or yellow)?

Answer 1

Concepts and reason

The main concept required to solve this problem is the interference, wavelength, refractive index, and thickness.

Initially, write the equation for constructive interference. Use this equation and calculate the wavelength of the light for the first and second order and find the colour of the light.

Fundamentals

The equation for the constructive interference is,

$2nd = \left( {m + \frac{1}{2}} \right)\lambda$

Here, n is the refractive index, d is the thickness, m is the number of orders, and $\lambda$ is the wavelength of the light.

The equation for the constructive interference is,

$2nd = \left( {m + \frac{1}{2}} \right)\lambda$

Here, n is the refractive index of the water, d is the thickness of the soap bubble, and $\lambda$ is the wavelength of the visible light.

Rearrange the above equation for $\lambda$ .

$\lambda = \frac{{2nd}}{{\left( {m + \frac{1}{2}} \right)}}$ …… (1)

For m = 1,

Substitute 1.33 for n, 390 nm for d, and 1 for m in above equation (1).

$\begin{array}{c}\\\lambda = \frac{{2\left( {1.33} \right)\left( {390{\rm{ nm}}\left( {\frac{{{{10}^{ - 9}}{\rm{ m}}}}{{1{\rm{ nm}}}}} \right)} \right)}}{{\left( {1 + \frac{1}{2}} \right)}}\\\\ = 691 \times {10^{ - 9}}{\rm{ m}}\left( {\frac{{1{\rm{ nm}}}}{{{{10}^{ - 9}}{\rm{ m}}}}} \right)\\\\ = 691{\rm{ nm}}\\\end{array}$

For m = 2,

Substitute 1.33 for n, 390 nm for d, and 2 for m in above equation (1).

$\begin{array}{c}\\\lambda = \frac{{2\left( {1.33} \right)\left( {390{\rm{ nm}}\left( {\frac{{{{10}^{ - 9}}{\rm{ m}}}}{{1{\rm{ nm}}}}} \right)} \right)}}{{\left( {2 + \frac{1}{2}} \right)}}\\\\ = 415 \times {10^{ - 9}}{\rm{ m}}\left( {\frac{{1{\rm{ nm}}}}{{{{10}^{ - 9}}{\rm{ m}}}}} \right)\\\\ = 415{\rm{ nm}}\\\end{array}$

The wavelength of the visible light 691 nm gives the colour of red.

The wavelength of the visible light 415 nm gives the colour of violet.

The sum of the colours red and violet gives the purple colour.

Therefore, the soap bubble appears to be purple colour.

Ans:

The wavelengths of the visible light are 691 nm and 415 nm.

The soap bubble appears to be purple color.

Answer 2

given thatthick ness of soap bubble t = 390 nm

a) 2nd + λ/2 = nλ
b) 2nd = (n- 1/2)λλ = 2nd/(n - 1/2)= 1037/(n - 1/2) nm
n= 1, λ > 760 nm
n= 2, λ = 691 nm (red)
n= 3, λ = 415 nm (violet)