Question

In a YDSE experiment, I₀ is given to be the intensity of the central bright fringe &b is the fringe width. Then, at a distance y from central bright fringe, the intensity will be –

• A. I₀cos $\left( \frac{\pi y}{\beta} \right)$
• B. $I_{0}\cos^{2}\left( \frac{\pi y}{\beta} \right)$
• C. $I_{0}\cos\left( \frac{2\pi y}{\beta} \right)$
• D. $I_{0}\cos^{2}\left( \frac{\pi y}{2\beta} \right)$

Answer 1

Answer: (B)

$I_{0}\cos^{2}\left( \frac{\pi y}{\beta} \right)$

Answer 2

Dx = $\frac{y}{\beta}$ ̃ Df = $\frac{2\pi}{\lambda}$ × Dx = $\frac{2\pi y}{\beta}$

I_net = I + I + 2I cos Df

= 2I$\left( 1 + \cos\left( \frac{2\pi y}{\beta} \right) \right)$ = 4I cos²$\left( \frac{\pi y}{\beta} \right)$

= I₀ cos² $\left( \frac{\pi y}{\beta} \right)$ [Q I₀ = 4I]