Chapter 11.6, Problem 2cT

Consider light incident on a thin soap film, as illustrated in the cross-sectional side view diagram at right.

The soap film is supported by a loop (not shown), which is held vertically. Only a small portion of the film has been shown; the thickness of the film is greatly exaggerated.

In answering the following questions, use an analogy between this situation and the connected spring in parts A and B.

1. Reflection and transmission at the first boundary

a. On the diagram, draw rays that correspond to the light is transmitted and reflected at the first boundary (on the left)?

b. Is the frequency of the transmitted wave (in the film) greater than, less than, or equal to the frequency of the incident wave (in the air)?

c. Is the wavelength of the transmitted wave (in the film) greater than, less than, or equal to the wavelength of the incident wave (in the air)?

d. For light incident on the first boundary, would the reflection at this boundary be more like reflection from a fixed end or from a free end? Explain.

e. On the basis of your answers above:

At the first boundary, would the reflected wave be in phase or $180°$ out of phase with the incident wave (i.e., is there a phase change upon reflection)?

At the first boundary, would the transmitted wave be in phase or $180°$ out of phase with the incident wave (i.e., is there a phase change upon transmission)?

Reflection at the second boundary

a. Continue the transmitted ray (from part 1) through the film to the second boundary (on the right), Then draw rays that correspond to the light that is transmitted and reflected at the second boundary.

b. For light incident on the second boundary, would the reflection at this boundary he more like reflection from a fixed end or from free end? Explain.

At the second boundary, would the reflected wave be in phase or $180°$ out of phase with the incident wave (in the film)?

3. Transmission at the first boundary

Continue the reflected ray from part 2 through the film back to the first boundary. Then draw rays that correspond to the light that is transmitted and reflected at this boundary.

Would there be a phase change on transmission at this boundary?