Question

A scientist directs monochromatic light toward a single slit in an opaque barrier. The light has a wavelength of 580 nm and the slit is 0.215 mm wide. The light that passes through the slit creates a diffraction pattern on a screen, which is 1.80 m from the slit. (a) How wide (in mm) is the central maximum (the central, bright fringe), as measured on the screen? ______ mm
(b) How wide (in mm) is either of the two first-order bright fringes, as measured on the screen? ______ mm

Answer 1

Answer:

a) 9.72 mm

b) 4.86 mm

Explanation:

wave length of light  λ is  580 nm = 580 \times 10⁻⁹ m

Width of slit d = 0.215\times 10⁻³ m

Distance of screen D  = 1.8 m.

Width of one fringe = $\frac{\lambda\times D}{d}$

Putting the values we get fringe width

= $\frac{580\times10^{-9}\times1.8}{.000315}$

=4.86 mm.

a) Width of central maxima = 2 times width of one fringe

= 2 times 4.86

=9.72 mm

b) width of each fringe except central fringe  is same , no matter what the order is.Only brightness changes .

So width of either of the two first order bright fringe will be same and it will be  

= 4.86 mm.