Question

Soap bubbles can display impressive colors, which are the result of the enhanced reflection of light of particular wavelengths from the bubbles' walls. For a soap solution with an index of refraction of 1.29, find the minimum wall thickness that will enhance the reflection of light of wavelength 709 nm in air.

Answer 1

The value is
`t = 1.374 *10^(-7) \ m`

Step-by-step explanation:

From the question we are told that

The refractive index is
`\mu = 1.29`

The wavelength is
`\lambda = 709 \ nm = 709 *10^(-9) \ m`

Generally the condition for constructive interference is

`2 * \mu * t = (n - (1)/(2) )\lambda`

At minimum thickness(t) the order of the fringe(n) will be equal to 1

So

`2 * 1.29 * t = (1 - (1)/(2) )* 709 *10^(-9)`

=>
`t = 1.374 *10^(-7) \ m`