Light of wavelength 638 nm falls onto a single slit 4.40 x 10^-4 m wide, producing a diffraction pattern on a screen 1.45 m away. Determine the width of the central fringe.
When monochromatic, coherent light passes through a single slit a series of bright and dark fringes are created on a screen on the other side.
The position of the minima are given by the relation `m*lambda = a*sin theta_m` `` where is the wavelength of light, and a is the width of the slit.
Here, the screen is placed at a distance of 1.45 m. This allows `sin theta_m` `` to be approximated by `y_m/L` `` . The width of the central maximum is given by the distance between `y_1` and `y_(-1)` `` . This is equal to `(2*L*lambda)/a` ``
Substituting L = 1.45 m, `lambda` = 638*10^-9 m and a = 0.44*10^-3 m, the width of the central maximum is `(2*1.45*638*10^-9)/(0.44*10^-3) = 4.205*10^-3 m`