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## Sunday, 7 August 2011

### Physics GRE - #6

A soap film with index of refraction greater than air is formed on a circular wire that is held in a vertical plane. The film is viewed by reflected light from a white-light source. Bands of color are observed at the lower parts of the soap film, but the area near the top appears black. A correct explanation for this phenomenon would involve which of the following?

1. The top of the film absorbs all of the light incident on it; none is transmitted.
2. The thickness of the top part of the film has become much less than a wavelength of visible light.
3. There is a phase change of 180 degrees for all wavelengths of light reflected from the front surface of the film.
4. There is no phase change for any wavelength of light reflected from the back surface of the film.

• 1 only.
• 2 and 3 only.
• 3 and 4 only.
• 1, 2, and 3.
• 2, 3, and 4.

Solution :

2, 3, and 4 are true.

The light produced from the soap film is due to interference of the rays reflecting from the back of the film and the rays reflecting from the front of the film. Due to gravity, most of the water in the soap film sinks to the bottom, leaving a film much thinner than the wavelength of visible light at the top (2).

Because there is a phase change of 180 degrees for rays reflected at the front surface (3) and no phase change for rays reflected at the back surface (4), the path difference between these two reflected rays is essentially zero while the phase difference is 180 degrees. Thus, the front and back rays cancel each other out and so there is no reflection. The combination of 2, 3, and 4 is what makes any thin film transparent. This means that the thin film essentially allows light to pass through without absorption (thus 1 is false).

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