Question

A soap film in the air has a thickness of $175$ nm. If the index of refraction of the soap film is $1.35$, what colour of light will be transmitted through? (i.e, What colour does the bubble appear to be from the other side?)

Answer 1

Given: A soap film in the air has a thickness of 175 nm. If the index of refraction of the soap film is 1.35,

To find the colour of light will be transmitted through and what colour does the bubble appear to be from the other side

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.

In order for constructive interference to occur in the transmission, the path length difference must be $l$, so that the film thickness must be $\frac{\lambda }{2}$. Thus, the wavelength of the light in the film is double the thickness of the film.

And as per the given criteria,

${\mu }_{film}=1.35,t_{film}=175nm$

We know,

${\lambda }_{film}=2t⟹{\lambda }_{film}=2\times 175nm⟹{\lambda }_{film}=350nm$

now,

${\mu }_{film}=\frac{{\lambda }_{air}}{{\lambda }_{film}}⟹{\lambda }_{air}=1.35\times 350nm⟹{\lambda }_{air}=472.5nm$

Light with wavelength 473nm will be transmitted through and it is the wavelength of blue color.

The reflected light is weak in the red region of the spectrum and strong in the blue-violet region. The soap film will, therefore, possess a pronounced blue colour.