Researcher measures the thickness of a layer of benzene (n = 1.50) floating on water by shining monochromatic light onto the film and varying the wavelength of the light. She finds that light of wavelength 585 nm is reflected most strongly from the film.

A: What does she calculate for the minimum thickness of the film?

Minimum thickness; t = 9.75 x 10^ (-8) m

Explanation:

We are given;

Wavelength of light; λ = 585 nm = 585 x 10^ (-9) m

Refractive index of benzene; n = 1.5

Now, let's calculate the wavelength of the film;

Wavelength of film; λ_film = Wavelength of light/Refractive index of benzene

Thus; λ_film = 585 x 10^ (-9) / 1.5

λ_film = 39 x 10^ (-8) m

Now, to find the thickness, we'll use the formula;

2t = ½m (λ_film)

Where;

t is the thickness of the film

m is an integer which we will take as 1

Thus;

2t = ½ x 1 x 39 x 10^ (-8)

2t = 19.5 x 10^ (-8)

Divide both sides by 2 to give;

t = 9.75 x 10^ (-8) m