Question

A soap bubble has a thickness of $100nm$ and a refractive Index of $1.35$. Given that the wavelength of red light is about $700nm$ and that of blue light is $400nm$, what colour does the bubble appear to be at the point on its surface closest to an observer when it is illuminated by white light?

• A. White
• B. Black
• C. Red
• D. Green

Answer 1

The correct option is D Green

Given: A soap bubble has a thickness of 100 nm and a refractive Index of 1.35. Given that the wavelength of red light is about 700 nm and that of blue light is 400 nm,

To find what colour does the bubble appear to be at the point on its surface closest to an observer when it is illuminated by white light

Solution:

The light will be transmitted through the soap bubble occurs for same condition as for minimum reflection and the transmitted light will be in phase with the incident light (phase is never inverted on transmission).

The light reflected from the internal surface will also be in phase with the incident light.

the film thickness must be $\frac{\lambda }{4}$.

And as per the given criteria,

${\mu }_{film}=1.35,t_{film}=100nm$

We know,

${\lambda }_{film}=4t⟹{\lambda }_{film}=2\times 100nm⟹{\lambda }_{film}=400nm$

now,

${\mu }_{film}=\frac{{\lambda }_{air}}{{\lambda }_{film}}⟹{\lambda }_{air}=1.35\times 400nm⟹{\lambda }_{air}=540nm$

Light with wavelength 540nm will be transmitted through and it is the wavelength of green color.

The soap film will, therefore, possess a pronounced green colour.