Question

The Young's double-slit experiment is performed with the light of blue colour \((\lambda_b = 4350\,\text{\AA})\) and then with green colour \((\lambda_g = 5450\,\text{\AA})\). Without changing the experimental setup, if the distance of the sixth fringe from the centre is determined for both the colours as \(x_{\text{blue}}\) and \(x_{\text{green}}\), then \(x_{\text{blue}} : x_{\text{green}}\) is nearly

• A. \(0.2\)
• B. \(1 : 2\)
• C. \(0.8\)
• D. \(1 : 5\)

Hint:

In Young’s double-slit experiment, fringe separation and fringe positions are directly proportional to wavelength.

Answer 1

The Correct Option is C

Step 1: Fringe position formula.
In YDSE, the position of the \(n\)-th bright fringe is given by:
\[ x_n = n\frac{\lambda D}{d} \]
Step 2: Ratio of fringe positions.
For the same experimental setup and same fringe order,
\[ \frac{x_{\text{blue}}}{x_{\text{green}}} = \frac{\lambda_b}{\lambda_g} \]
Step 3: Substitute wavelength values.
\[ \frac{x_{\text{blue}}}{x_{\text{green}}} = \frac{4350}{5450} \]
Step 4: Numerical evaluation.
\[ \frac{4350}{5450} \approx 0.8 \]
Step 5: Conclusion.
The ratio \(x_{\text{blue}} : x_{\text{green}}\) is nearly \(0.8\).