Question

A beam of light (\( \lambda = 600 \, \text{nm} \)) from a distant source, falls on a single slit 1 mm wide and the resulting diffraction pattern is observed on a screen 2 m away. The distance between the first dark fringes on either side of the central bright fringe is:

• A. 1.2 cm
• B. 1.2 mm
• C. 2.4 cm
• D. 2.4 mm

Hint:

In diffraction problems, the angular position of the first dark fringe is directly related to the wavelength and the slit width. For small angles, the linear distance can be approximated by multiplying the angular displacement by the screen distance.

Answer 1

The Correct Option is D

In single-slit diffraction, the angular position of the first dark fringe is given by: \[ \sin \theta = \frac{\lambda}{a} \] where \( \lambda \) is the wavelength of light and \( a \) is the width of the slit.
For small angles, \( \sin \theta \approx \theta \). The distance between the dark fringes on either side of the central bright fringe is given by: \[ y = 2L \tan \theta \approx 2L \theta \] where \( L \) is the distance from the slit to the screen, and \( y \) is the distance between the dark fringes. Substituting the given values: \[ \theta = \frac{\lambda}{a} = \frac{600 \times 10^{-9}}{1 \times 10^{-3}} = 6 \times 10^{-4} \, \text{radians} \] \[ y = 2 \times 2 \times 6 \times 10^{-4} = 2.4 \times 10^{-3} \, \text{m} = 2.4 \, \text{mm} \]
Thus, the correct answer is (d).