# A soap bubble is essentially a thin film of water surrounded by air. The colors you see in soap...

## 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?

## Interference of Wave:

The phenomenon in which two separate waves initiated from two coherent sources meet each other, combine and form a new wave of lower of higher magnitude s known as interference.

Given Data

• The thickness of soap bubble is: {eq}t = 390\;{\rm{nm}} {/eq}

The expression for constructive wavelength from constructive interference is as follows.

{eq}\lambda = \dfrac{{4nt}}{{\left( {2m + 1} \right)}} {/eq}

Here, the order is m, the refractive index is n and wavelength of visible of light is {eq}\lambda {/eq}

The value of refractive index for soap bubble is 1.33.

{eq}n = 1.33 {/eq}

Calculate the wavelength for m=1

{eq}\begin{align*} \lambda &= \dfrac{{4nt}}{{\left( {2 \times 1 + 1} \right)}}\\ \lambda &= \dfrac{{4 \times 1.33 \times 390\;{\rm{nm}}}}{3}\\ \lambda &= 691.6\;{\rm{nm}} \end{align*} {/eq}

Calculate the wavelength for m=2

{eq}\begin{align*} \lambda &= \dfrac{{4nt}}{{\left( {2 \times 2 + 1} \right)}}\\ \lambda &= \dfrac{{4 \times 1.33 \times 390\;{\rm{nm}}}}{5}\\ \lambda &= 414.9\;{\rm{nm}} \end{align*} {/eq}

Calculate the wavelength for m=3

{eq}\begin{align*} \lambda &= \dfrac{{4nt}}{{\left( {2 \times 3 + 1} \right)}}\\ \lambda &= \dfrac{{4 \times 1.33 \times 390\;{\rm{nm}}}}{7}\\ \lambda &= 296.4\;{\rm{nm}} \end{align*} {/eq}

For m=3 the wavelength value is shorter than 390 nm.

Thus, the visible wavelengths of light that are reflected are {eq}691.6\;{\rm{nm}} {/eq} and {eq}414.9\;{\rm{nm}} {/eq} respectively.

The color corresponding to wavelength {eq}691.6\;{\rm{nm}} {/eq} is reddish and for {eq}414.9\;{\rm{nm}} {/eq} is violet. Therefore the soap bubble appears in purple color (combination of reddish and purple).