Question

Consider Young's experiment where two narrow slits are 0.40 mm apart from center to center. The irradiance at each slit is 0.25 W/m^2. Fringes separated by 3.40 mm appear on a screen 2.00 mm away. Write an expression for the irradiance at the screen as a function of x, the displacement from the central axis.

Answer 1

As per the given question,

distance between the two slit (d)=0.4mm

Radiations $(I)=0.25W/m^2$

The separation between the fringes y=3.40mm

screen distance D=2mm

$y=\dfrac{\lambda D}{d}$

$\Rightarrow \lambda = \dfrac{yd}{D}$

$\Rightarrow \lambda = \dfrac{3.40\times 0.4}{2}=0.68mm$

$\phi = \dfrac{2\pi}{\lambda}x=\dfrac{2\pi}{0.68}x$

$I=I_o \cos^2\phi=0.25 \cos(\dfrac{2\pi}{0.68})x$