Question

In a Young's double slit experiment the angular width of a fringe formed on a distant screen is \( 1^\circ \). The wavelength of the light used is \( 6280 \, \text{Å} \). What is the distance between the two coherent sources?

• A. 0.036 mm
• B. 0.12 mm
• C. 6 mm
• D. 4 mm

Hint:

The distance between the slits in Young’s double slit experiment can be found using the angular width of the fringe and the wavelength.

Answer 1

The Correct Option is A

Step 1: Angular width of fringe.
The angular width of the fringe in Young’s double slit experiment is given by: \[ \theta = \frac{\lambda}{d} \] where \( \lambda \) is the wavelength of the light and \( d \) is the distance between the two slits.

Step 2: Solve for \( d \).
Given that \( \theta = 1^\circ \), \( \lambda = 6280 \, \text{Å} = 6.28 \times 10^{-7} \, \text{m} \), and converting the angle to radians, we get: \[ d = \frac{\lambda}{\theta} = \frac{6.28 \times 10^{-7}}{\tan(1^\circ)} = 0.036 \, \text{mm} \] Thus, the correct answer is (1).