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7.1 THE NATURE OF LIGHT

P71 016

This question is about thin film interference. The phenomenon of thin film interference is an excellent example which provides experimental evidence for the wave nature of light.

The question is from the 1989 HSC Physics Examination. It is a very good question because it brings together many wave properties.

A very thin film of oil of refractive index 1.40 and thickness 2.25 nm is illuminated normally with blue light of wavelength 420 nm in air. The oil film is on a glass surface as shown below.

The light is partially reflected from both the oil surface and the oil-glass boundary.

(A)

Calculate the wavelength of the light in oil.

(B)

Calculate the optical path difference between the two reflections (air-oil and oil-glass).

(C)

What is the change in phase of the wave when reflected from the air-oil boundary and the oil-glass boundary?

(D)

What effect results for these two reflections?

(E)

How would you answer to part (D) be changed if the second material was not glass but one of refractive index 1.20? Explain your answer.

View solution below only after you have completed answering the question. The solution is not in a form that you would answer in an examination. The answers are often in more detail to help improve your appreciation and understanding of the physics.

Solution

You need to draw an annotated diagram of the situation

(A)

The frequency of the wave in the air, oil and glass is the same

The velocity of the wave in the oil is

The wavelength of the light in the oil is

(B)

The path difference between the two reflections is 2d. The reflection from oil-glass boundary travels a distance 2d through the oil.

The optical path difference is

(C)

When a wave strikes a boundary than is ‘more dense’, the reflected wave has a phase change of rad. view animations

Both reflected waves are reflected from a medium of higher refractive index (optically more dense) so both reflections have a rad change of phase.

(D)

The two reflections interfere with each other. The optical path difference between the two reflections is wavelengths and both reflected waves undergo a rad change of phase. Hence, the waves will be out of phase and interfere destructively.

destructive interference dark reflection

view animations

(E)

If the second reflection is from a medium which has a refractive index less than oil (1.40 < 1.20) then the reflected wave has zero change in phase. Hence, the two reflected waves will be a multiple of a wavelength out of phase (the waves will be in phase) and they will interfere constructively.

constructive interference bright reflection