Question

As the thickness of a soap bubble increases under sunlight, which colour appears later?

• A. Violet
• B. Blue
• C. Green
• D. Red

Hint:

A simple way to remember this: Thin film (to) Short (lambda) colors appear (V, B). Thick film (to) Long (lambda) colors appear (O, R). This question asks about increasing thickness, so the color sequence follows the VIBGYOR order.

Answer 1

The Correct Option is D

Step 1: Understanding the Question: The question asks which color in the visible spectrum will appear "later" as the thickness of a soap film increases from a very small value. "Later" implies at a greater thickness.

Step 2: Key Formula or Approach: The bright colors seen in a soap bubble are due to the constructive interference of light waves reflecting from the front and back surfaces of the thin film. The condition for constructive interference for a specific wavelength (lambda) is given by: [ 2nt = left(m + frac{1}{2}right)lambda ] where:
• (n) is the refractive index of the soap film.
• (t) is the thickness of the film.
• (m) is an integer (0, 1, 2, ...), representing the order of the interference.
• (lambda) is the wavelength of the light.

Step 3: Detailed Explanation: From the formula, for a fixed order of interference (e.g., for the first-order colors, (m=0)), the thickness (t) required to produce a bright color is directly proportional to the wavelength (lambda). [ t = frac{(m + 1/2)lambda}{2n} implies t propto lambda ] The visible spectrum, ordered by increasing wavelength, is: Violet (to) Blue (to) Green (to) Yellow (to) Orange (to) Red (Shortest Wavelength) (to) (Longest Wavelength) As the thickness (t) of the film gradually increases from near zero:
• The condition for constructive interference will first be met for the shortest wavelength, which is violet/blue.
• As (t) continues to increase, the condition will then be met for green, then yellow, and so on.
• The color with the longest wavelength, red, will require the greatest thickness to be seen for the same order of interference. Therefore, red appears later than the other colors listed.

Step 4: Final Answer: Since the required thickness for constructive interference is proportional to the wavelength, red, having the longest wavelength among the given options, will appear at a greater thickness, i.e., "later".