Question

White light is shining on the surface of a soap bubble, which has the same index of refraction as water. Find the minimum thickness, in nanometers, of a soap bubble which appears red (a wavelength of 725 nm) when the light is perpendicular to its surface.

Answer 1

The minimum thickness is
`t = 1.363 *10^(-7) \ m`

Step-by-step explanation:

From the question we are told that

The index of refraction of the bubble is
`n = 1.33` = index of refraction of water

The wavelength is
`\lambda =725nm = 725 *10^(-9) \ m`

Generally the condition for constructive interference is mathematically represented as

`2 * t = [m + (1)/(2) ] * (\lambda )/(n)`

Now t is the thickness and at minimum t, m(order of maximum ) = 0

So

`2 * t = [0 + (1)/(2) ] * ( 725 *10^(-9) )/( 1.33)`

=>
`t = 1.363 *10^(-7) \ m`