Question

In a biprism experiment, red light of wavelength $6500\,\text{Å}$ was used. It was then replaced by green light of wavelength $5200\,\text{Å}$. The value of $n$ for which the $(n+1)^{\text{th}}$ green bright band would coincide with $n^{\text{th}}$ red bright band for the same setting is: 

• A. \( n = 5 \)
• B. \( n = 3 \)
• C. \( n = 4 \)
• D. \( n = 2 \)

Hint:

In interference experiments, fringe widths depend on the wavelength of light. Use the relationship between the wavelengths of the two lights to calculate when the bands coincide.

Answer 1

The Correct Option is C

Step 1: Condition for Coincidence of Bright Bands.
For the green and red light bands to coincide, their path difference should be equal. The fringe width for red and green light is proportional to the wavelength, and using this relationship, we can determine the value of \( n \) for which the bright bands coincide. By equating the path differences and solving for \( n \), we find that \( n = 4 \).
Step 2: Final Answer.
Thus, the value of \( n \) is 4.