Question

A thin film of oil (n = 1.38) of thickness 432 nm with air on both sides is illuminated with white light at normal incidence. Determine the most strongly and the most weakly reflected wavelengths in the range 374 nm to 506 nm. (Enter your answers in nm.)

Answer 1

When white light passes through a thin film, the different wavelengths of light interfere with each other. By calculating the minimum thickness of the film for constructive interference, we can determine the most strongly and most weakly reflected wavelengths.

When white light passes through a thin film, the different wavelengths of light interfere with each other. The most strongly reflected wavelengths occur when the path difference between the two reflected waves is an integer multiple of the wavelength. The formula to calculate the wavelength that undergoes maximum constructive interference is given by:

2nt = mλ

where n is the refractive index of the film, t is the thickness of the film, m is an integer, and λ is the wavelength of light. By rearranging the formula, we can find the minimum thickness of the film for constructive interference:

t = (mλ) / (2n)

Using this formula, we can calculate the most strongly and most weakly reflected wavelengths for the given problem.

Answer 2

Step-by-step explanation:

Given that,

Thickness = 432 nm

n = 1.38

We need to calculate the value of 2nt

For dark fringe,

`2nt=m\lambda`

For bright fringe

`2nt=(m+(1)/(2))\lambda`

Put the value into the formula of bright fringe

`2nt=2*1.38* 432*10^(-9)=1192.32*10^(-9)`

We need to calculate the wavelength

(a). For strongly reflected

`\lambda=(2nt)/(m+(1)/(2))`

Put the value into the formula

`\lambda=(1192.32*10^(-9))/(2+(1)/(2))`

Here, m = 2

`\lambda=4.77*10^(-7)=477\ nm`

We need to calculate the wavelength

(b). For weakly reflected

`\lambda=(2nt)/(m)`

Put the value into the formula

`\lambda=(1192.32*10^(-9))/(2)`

Here, m = 2

`\lambda=5.96*10^(-7)=596\ nm`

Hence, This is the required solution.