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

a) 9.72 mm

b) 4.86 mm

Step-by-step 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 =
`(\lambda* D)/(d)`

Putting the values we get fringe width

=
`(580*10^(-9)*1.8)/(.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.