Two slits speet 0.25 mm apart are placed 0.75 m from a screen and illuminated by coherent light with a wavelength of 650 nm. The intensity at the center of the central maximum `(theta = 0^(@))` is `I_(0)`. The distance on the screen from the center of the central maximum to the point where the intensity has fallen to `I_(0) // 2` is nearly

Options

A. 0.1 nmn
B. .25 mm
C. 0.4 mm
D. 0.5 mm

Answer

d

Explanation

`I = I_(0) cos^(2) (((lambda d sin theta))/(lambda)) = (I_(0))/(2)`
`cos ((pi d sin theta)/(lambda)) = (1)/(sqrt 2)`
`x = (lambda D)/(4 d) = (650 xx 10^(-9) xx 0.75)/(4 xx 0.25 xx 10^(-3))`
` = 487.5 xx 10^(-6)m`
`= 0.4875 mm ~~ 0.5 mm`