The central bright fringe in a single slit diffraction patte

The central bright fringe in a single slit diffraction pattern from light of wavelength 541 nm is 2.70 cm wide on a screen that is 1.400 m from the slit. How wide is the slit? How wide are the first two bright fringes on either side of the central bright fringe? (Define the width of a bright fringe as the linear distance from minimum to minimum.)

Solution

Width of central fringe=(2y1)=0.027 m

y1=0.0135 m

x=1.4 m

Lamda=541*10^-9 m

a)Slit width a =x(Lamda)/y1

=1.4 m(541*10^-9 m)/0.0135 m

=5.61*10^-5 m

=0.0561 mm

b)

Both fringes are on either side of central bright fringe is,

=1.35 cm