Question

In biprism experiment, if 5th bright band with wavelength \( \lambda_1 \) coincides with 6th dark band with wavelength \( \lambda_2 \), then the ratio \( \frac{\lambda_2}{\lambda_1} \) is

• A. \( \frac{10}{11} \)
• B. \( \frac{7}{9} \)
• C. \( \frac{11}{10} \)
• D. \( \frac{9}{7} \)

Hint:

In biprism experiments, the fringe width is related to the wavelength of the light used, so the ratio of wavelengths corresponds to the ratio of fringe widths.

Answer 1

The Correct Option is A

Step 1: Using the fringe width formula.
The fringe width for a biprism experiment is given by the formula: \[ \beta = \frac{\lambda D}{d} \] where \( \lambda \) is the wavelength, \( D \) is the distance between the slits and the screen, and \( d \) is the distance between the slits. The 5th bright band with \( \lambda_1 \) coincides with the 6th dark band with \( \lambda_2 \).
Step 2: Applying the relation.
The ratio of the wavelengths is: \[ \frac{\lambda_2}{\lambda_1} = \frac{10}{11} \] Step 3: Conclusion.
Thus, the correct answer is (A), \( \frac{10}{11} \).