Question

Two straight narrow parallel slits 3mm apart are illuminated by a

monochromatic light of wavelength 590nm. Fringes are obtained on a

screen 90 cm away from the slits. Calculate the fringe width​

Answer 1

Given:

distance between two narrow slits d = 3 mm

wavelength of monochromatic light λ = 590 nm

fringes obtained at a distance D = 90 cm

To find:

fringe width​ β =?

Step-to-step-explanation:

• Two straight narrow parallel slits are 3mm apart are illuminated by a monochromatic light of wavelength 590nm.
• The fringes were obtained at a distance of 90cm away from the slits.
• We have to find the fringe width​.
• The fringe width obtained by monochromatic light is given by:

          $\displaystyle \beta = \frac{\lambda\ D}{d}$

          where

          β  = fringe width

          λ = wavelength of monochromatic light

         D = fringes obtained at a distance away from the screen

         d = distance between two narrow slits

• Put the given values in the above equation to find the fringe width​.

         $\displaystyle \beta = \frac{590\times 10^{-9} \times 90 \times 10^{-2}}{3\times 10^{-3}}$

             = 1.77 × 10⁻⁴

             = 0.177  × 10⁻³

          β = 0.177 mm

• Hence, the fringe width​ is 0.177 mm.