Question

Young’s double-slit experiment is carried out by using green, red and blue lights, one at a time. The fringe widths recorded are \( \beta_G \), \( \beta_R \) and \( \beta_B \) respectively. Then

• A. \( \beta_G<\beta_R<\beta_B \)
• B. \( \beta_B<\beta_R<\beta_G \)
• C. \( \beta_G<\beta_B<\beta_R \)
• D. \( \beta_B<\beta_G<\beta_R \)
• E. \( \beta_G = \beta_R = \beta_B \)

Hint:

The fringe width is directly proportional to the wavelength of the light. Hence, for shorter wavelengths, the fringe width will be smaller.

Answer 1

The Correct Option is D

The fringe width in Young’s double-slit experiment is given by the formula: \[ \beta = \frac{\lambda D}{d} \] 
where: 
- \( \lambda \) is the wavelength of the light, 
- \( D \) is the distance between the screen and the slits, 
- \( d \) is the distance between the slits. 
Since the wavelength of blue light (\( \lambda_B \)) is smaller than that of green (\( \lambda_G \)) and red (\( \lambda_R \)) light, the fringe width follows the order: \[ \beta_B<\beta_G<\beta_R \] 
Hence, the correct answer is (D).