Question

A thin soap bubble of index of refraction 1.33 is viewed with light of wavelength 550.0nm and appears very bright. Predict a possible value of the thickness of the soap bubble.

Answer 1

Answer:

The possible thickness of the soap bubble = $1.034\times 10^{-7}\ m.$

Explanation:

Given:

• Refractive index of the soap bubble, $\mu=1.33.$
• Wavelength of the light taken, $\lambda = 550.0\ nm = 550.0\times 10^{-9}\ m.$

Let the thickness of the soap bubble be $t$.

It is given that the soap bubble appears very bright, it means, there is a constructive interference takes place.

For the constructive interference of light through a thin film ( soap bubble), the condition of constructive interference is given as:

$2\mu t=\left ( m+\dfrac 12 \right )\lambda.$

where $m$ is the order of constructive interference.

Since the soap bubble is appearing very bright, the order should be 0, as $0^{th}$ order interference has maximum intensity.

Thus,

$2\mu t=\left (0+\dfrac 12\right )\lambda\\t=\dfrac{\lambda}{4\mu}\\\ \ = \dfrac{550\times 10^{-9}}{4\times 1.33}\\\ \ = 1.034\times 10^{-7}\ m.$

It is the possible thickness of the soap bubble.