Question

The number of bright fringes formed due to interference on 1 m of screen placed at \(\frac{4}{3}\) m away from the slits is:

• A. \(2\)
• B. \(3\)
• C. \(6\)
• D. \(10\)

Hint:

The theoretical number of fringes can be very high, but practical visibility and resolution limitations typically reduce the number that can be distinctly observed and counted on the screen.

Answer 1

The Correct Option is D

Given: \begin{itemize} \item Screen distance \( D = \frac{4}{3} \, m} \) \item Screen length \( L = 1 \, m} \) \item Wavelength \( \lambda = 450 \, nm} = 0.45 \times 10^{-6} \, m} \) \item Distance between slits \( d = 6 \, \mum} = 6 \times 10^{-6} \, m} \) \end{itemize} The fringe spacing \( \Delta y \) is calculated using the formula: \[ \Delta y = \frac{\lambda D}{d} \] Substituting the given values: \[ \Delta y = \frac{0.45 \times 10^{-6} \times \frac{4}{3}}{6 \times 10^{-6}} = 0.1 \, m} \] The number of fringes in \( 1 \, m} \) is: \[ \frac{L}{\Delta y} = \frac{1}{0.1} = 10 \] Therefore, the number of bright fringes formed on the screen is: \[ \boxed{10} \]