A very thin transparent film of soap bubble (thickness → 0) is seen under reflection of white light. Then the colour of the film appear to be :

Question

Accepted Answer

When a very thin transparent film of soap bubble (with thickness approaching zero) is observed under the reflection of white light, it appears black. This phenomenon can be explained through the principles of thin film interference.

1. **Explanation for Option 2 (Black):**
   - Thin film interference occurs when light waves reflected from the top and bottom surfaces of a thin film interfere with each other. For a film with negligible thickness (approaching zero), the path difference between the two reflected waves is minimal.
   - In such a case, the two reflected waves are nearly out of phase due to the phase change upon reflection from the denser medium (the air-soap interface). This results in destructive interference for all wavelengths of visible light.
   - Destructive interference means that the reflected light waves cancel each other out, leading to the absence of reflected light. As a result, the film appears black.

2. **Explanation for why other options are incorrect:**
   - **Option 1 (Blue):** If the film appeared blue, it would imply that constructive interference is occurring specifically for blue wavelengths while other wavelengths are destructively interfered. However, for a film with thickness approaching zero, destructive interference occurs for all wavelengths, not selectively for non-blue wavelengths.
   - **Option 3 (White):** A white appearance would suggest that all wavelengths of light are being constructively interfered and reflected equally. This is not possible for a film with negligible thickness, where destructive interference dominates.
   - **Option 4 (Yellow):** Similar to the explanation for blue, a yellow appearance would require constructive interference for yellow wavelengths. Again, with the film's thickness approaching zero, all wavelengths experience destructive interference, preventing any specific color from being reflected.

In conclusion, due to the destructive interference of all wavelengths of light in a very thin soap film, the film appears black, supporting Option 2 as the correct answer.