If the 8th bright band of wavelength \( \lambda_1 \) coincides with 9th bright band of wavelength \( \lambda_2 \) in a Young's double slits experiment then the possible wavelength of two lights are:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( \lambda_1 = 450\,\mathrm{nm},\ \lambda_2 = 400\,\mathrm{nm} \)
In Young's experiment the \( n \)th bright fringe lies at a distance \( y_n = n\lambda D/d \) from the centre. Two fringes coincide when they are at the same distance, with the same \( D \) and \( d \).
\( \displaystyle \frac{8\lambda_1 D}{d} = \frac{9\lambda_2 D}{d} \;\Rightarrow\; \frac{\lambda_1}{\lambda_2} = \frac{9}{8} \)
So \( \lambda_1 \) must be the longer wavelength. Checking the options:
\( \displaystyle \frac{450}{400} = \frac{9}{8} \)
Only Option (1) gives this ratio.