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The condition for dark fringes in single slit diffraction is given by
$\sin\theta = \frac{m\lambda}{a}$
in case, light from the entire slit arrives at point of observation in phase, for a bright band $\sin\theta$ is equal to:

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Single Slit Diffraction Bright Fringe Condition

In single-slit diffraction, the pattern of bright and dark fringes is formed due to the interference of light waves originating from different parts of the slit.

The condition for the central bright fringe is uniquely defined by the statement that "light from the entire slit arrives at the point of observation in phase". This occurs when the path difference from all parts of the slit to the observation point is zero. This happens directly opposite the center of the slit, corresponding to an angle of observation $\theta = 0$.

For the central bright fringe:

  • The angle $\theta = 0$.
  • Therefore, $\sin\theta = \sin(0) = 0$.

While the formula $\sin\theta = \frac{m\lambda}{a}$ is provided for dark fringes (minima), the condition for the central bright fringe (principal maximum) where light rays arrive in phase is always $\sin\theta = 0$.

Thus, for a bright band where light arrives in phase, $\sin\theta$ is equal to 0.

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