What is the minimum thickness of a thin film for maximum light reflection?

[Liquefaction]

1984 PHYSICS B WAVES

The surface of a glass plate (index of refraction n3 = 1.50) is coated with a transparent thin film (index of refraction n2 = 1.25). A beam of monochromatic light of wavelength 6.0 X 10-7 meter traveling in air (index of refraction n1 = 1.00) is incident normally on surface S1 as shown above. The beam is partially transmitted and partially reflected.

a) Calculate the frequency of the light.

b) Calculate the wavelength of the light in the thin film.

The beam of light in the film is then partially reflected and partially transmitted at surface S2·

c) Calculate the minimum thickness d1 of the film such that the resultant intensity of the light reflected back into the air is a minimum.

d) Calculate the minimum nonzero thickness d2 of the film such that the resultant intensity of the light reflected back into the air Is a maximum.

 

[physics girl phd]

You're going to have to show some of your own work first.

 

[kyle8921]

a) The frequency of the light can be calculated using the formula f = c/λ, where c is the speed of light (3.0 X 10^8 m/s) and λ is the wavelength of the light (6.0 X 10^-7 m). This gives us a frequency of approximately 5.0 X 10^14 Hz.

b) The wavelength of the light in the thin film can be calculated using the formula λ2 = λ1/n2, where λ1 is the wavelength of the light in air and n2 is the index of refraction of the thin film. Plugging in the values, we get a wavelength of approximately 4.8 X 10^-7 m.

c) To calculate the minimum thickness d1, we can use the formula d1 = λ2/4n2, where λ2 is the wavelength of the light in the thin film and n2 is the index of refraction of the thin film. This gives us a minimum thickness of approximately 1.9 X 10^-7 m.

d) To calculate the minimum nonzero thickness d2, we can use the formula d2 = λ2/2(n2-1), where λ2 is the wavelength of the light in the thin film and n2 is the index of refraction of the thin film. This gives us a minimum nonzero thickness of approximately 3.8 X 10^-7 m.