Condition for Overlapping Fringes:
In Young’s double slit experiment, the condition for overlapping fringes for different wavelengths is given by:
\[ n_2 \lambda_2 = n_1 \lambda_1 \]
where \( n_1 \) and \( n_2 \) are the fringe orders for wavelengths \( \lambda_1 \) and \( \lambda_2 \), respectively.
Determine the Ratio of Wavelengths:
Given:
\[ \lambda_1 = 450 \, \text{nm}, \quad \lambda_2 = 650 \, \text{nm} \]
The ratio of the wavelengths is:
\[ \frac{\lambda_1}{\lambda_2} = \frac{450}{650} = \frac{9}{13} \]
Find the Minimum Order of Overlapping Fringes:
For the fringes to overlap, \( n_2 \lambda_2 = n_1 \lambda_1 \).
Let \( n_1 = 13 \) and \( n_2 = 9 \) (the smallest integers that satisfy the ratio):
\[ n_2 = 9 \]
Conclusion:
The minimum order of fringe produced by \( \lambda_2 \) which overlaps with the fringe produced by \( \lambda_1 \) is \( n = 9 \).
Consider the sound wave travelling in ideal gases of $\mathrm{He}, \mathrm{CH}_{4}$, and $\mathrm{CO}_{2}$. All the gases have the same ratio $\frac{\mathrm{P}}{\rho}$, where P is the pressure and $\rho$ is the density. The ratio of the speed of sound through the gases $\mathrm{v}_{\mathrm{He}}: \mathrm{v}_{\mathrm{CH}_{4}}: \mathrm{v}_{\mathrm{CO}_{2}}$ is given by
Match List-I with List-II: List-I