If \( \beta_1, \beta_2 \) and \( \beta_3 \) are fringe widths for red, green and violet light respectively for the same setup of Young's double slit experiment, then
\( \beta_1 = \beta_2 = \beta_3 \)
\( \beta_1 > \beta_3 > \beta_2 \)
\( \beta_2 > \beta_1 > \beta_3 \)
\( \beta_1 > \beta_2 > \beta_3 \)
Solution:
The fringe width in Young's double slit experiment is given by \( \beta = \frac{\lambda D}{d} \), which is directly proportional to wavelength \( \lambda \). Since \( \lambda_{\text{red}} > \lambda_{\text{green}} > \lambda_{\text{violet}} \), we get \( \beta_1 > \beta_2 > \beta_3 \).
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