Question

Two children observe soap bubbles in sunlight. Initially the bubble appears bluish, but after some time it turns yellowish.
Which of the following statements are correct?
I. The colour shifts towards higher wavelength.
II. Blue/violet colours disappear earlier than red.
III. For sufficiently thick bubbles, the bubble appears white.

• A. I and II only
• B. II and III only
• C. I and III only
• D. I, II and III

Hint:

For thin-film interference, remember the relationship: thickness is proportional to the wavelength for constructive interference ((t propto lambda)). Thinning film (like a dying bubble): Color sequence shifts from red (to) yellow (to) blue (to) black (destructive interference for all wavelengths). Thickening film (like a newly formed bubble settling): Color sequence shifts from blue (to) green (to) yellow (to) red. The question describes a bubble thinning over time, so the color shift is towards red, but eventually all colors disappear starting from blue.

Answer 1

The Correct Option is D

Step 1: Understanding the Question: The question describes the changing colors of a soap bubble and asks which of the given statements about the phenomenon are correct. The color change is due to thin-film interference.

Step 2: Detailed Explanation: Analysis of Statement I: The colour shifts towards higher wavelength. The initial color is bluish (shorter wavelength) and it turns yellowish (longer wavelength). The visible spectrum in order of increasing wavelength is Violet-Indigo-Blue-Green-Yellow-Orange-Red (VIBGYOR). A shift from blue to yellow is indeed a shift towards a higher wavelength. Thus, statement I is correct.
Analysis of Statement II: Blue/violet colours disappear earlier than red.
The color seen is due to constructive interference, for which the condition (for near-normal incidence) is (2nt = (m + 1/2)lambda), where (n) is the refractive index, (t) is the film thickness, and
(lambda) is the wavelength. Over time, a soap bubble thins due to gravity and evaporation, so its thickness (t) decreases. As (t) becomes very small, it can no longer satisfy the constructive interference condition for any visible wavelength. Since blue/violet light has the shortest wavelength, it requires the smallest thickness to interfere constructively. As the film thins further, it becomes too thin even for blue light, causing it to "disappear" first, before the longer wavelengths like red. Thus, statement II is correct.
Analysis of Statement III: For sufficiently thick bubbles, the bubble appears white.
When the bubble film is very thick compared to the wavelengths of visible light (e.g., many micrometers), constructive and destructive interference occur for many different wavelengths across the visible spectrum at the same location. The reflected light is a mix of all these colors, and the combination of all colors of the spectrum appears as white light to the human eye. Thus, statement III is correct.

Step 3: Final Answer:
All three statements accurately describe phenomena related to thin-film interference in soap bubbles. Therefore, all three statements are correct.