White light is normally incident on a soap bubble in air, and the reflected light is viewed. As the wall thickness of the bubble approaches zero (just before it breaks) the reflected light

Options

A. Becomes dim for all wavelengths
B. Becomes unusually bright for all wavelengths
C. Becomes bright only for certain wavelengths, dependent on the index of refraction of the bubble
D. None of the above occurs

Answer

To solve the problem regarding the behavior of reflected light from a soap bubble as its wall thickness approaches zero, we can analyze the situation using the principles of thin film interference.

### Step-by-Step Solution:

1. **Understanding Thin Film Interference**:
- A soap bubble can be considered as a thin film of liquid with air on both sides. When white light strikes the bubble, some light is reflected off the top surface, and some is transmitted through the film and reflected off the bottom surface.

2. **Conditions for Interference**:
- The interference of light waves reflected from the two surfaces of the soap bubble can lead to constructive or destructive interference depending on the thickness of the film and the wavelength of light.
- The condition for destructive interference is given by:
\[ 2nd = (m + \frac{1}{2})\lambda \]
where \( n \) is the refractive index of the film, \( d \) is the thickness of the film, \( m \) is an integer (0, 1, 2,...), and \( \lambda \) is the wavelength of light.

3. **Effect of Decreasing Thickness**:
- As the thickness \( d \) approaches zero, the path difference between the two reflected waves also approaches zero. This means that the condition for constructive interference (where the waves reinforce each other) becomes more likely to be satisfied for all wavelengths.

4. **Reflection and Color Changes**:
- When the thickness of the soap bubble wall decreases, the reflected light will not show distinct colors (as seen in thicker soap bubbles) but will instead tend to reflect light more uniformly. This is because the condition for constructive interference is not met for specific wavelengths, leading to a dimming effect.

5. **Conclusion**:
- As the wall thickness approaches zero, the reflected light from the soap bubble will become dimmer and less colorful, approaching a uniform reflection of white light.

### Final Answer:
As the wall thickness of the bubble approaches zero, the reflected light becomes dimmer for all wavelengths.