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

The possible thickness of the soap bubble =
`1.034* 10^(-7)\ m.`

Step-by-step explanation:

Given:

• Refractive index of the soap bubble,
  `\mu=1.33.`
• Wavelength of the light taken,
  `\lambda = 550.0\ nm = 550.0* 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+\frac 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+\frac 12\right )\lambda\\t=(\lambda)/(4\mu)\\\ \ = (550* 10^(-9))/(4* 1.33)\\\ \ = 1.034* 10^(-7)\ m.`

It is the possible thickness of the soap bubble.