Question

In Young’s double slit experiment, the wavelengths of red and blue lights used are \(7.5 \times 10^{-5}\) cm and \(5 \times 10^{-5}\) cm respectively. If the \(n^{th}\) bright fringe of red color coincides with \((n+1)^{th}\) bright fringe of blue colour, then the value of \( n \) is

• A. 1
• B. 2
• C. 4
• D. 8

Hint:

Match fringe positions using wavelength and fringe number relationships in double slit experiment.

Answer 1

The Correct Option is B

Step 1: Fringe position formula
The position of bright fringes in double slit experiment is proportional to wavelength \( \lambda \) and fringe number \( n \): \[ y \propto n \lambda \] Step 2: Condition for coincidence
\[ n \lambda_{red} = (n+1) \lambda_{blue} \] Substitute values: \[ n \times 7.5 \times 10^{-5} = (n + 1) \times 5 \times 10^{-5} \] Step 3: Solve for \( n \)
\[ 7.5 n = 5 n + 5 \implies 2.5 n = 5 \implies n = 2 \] Step 4: Conclusion
The value of \( n \) is 2.