Monochromatic light from a narrow slit illuminates two narrow slits 0.3 mm apart, producing an interference pattern with bright fringes 1.5 mm apart on a screen 75 cm away. Find the wavelength of the light. How will the fringe width be altered if (a) the distance of the screen is doubled and (b) the separation between the slits is doubled?

Solution

Here,
Distance between the slits, d = 0.3 mm = 0.3 × 10^-3 m
Fringe width, β = 1.5 mm = 1.5 × 10^-3 m
distance between screen and the slit, D = 7.5 cm = 0.75 m

Wavelength λ is given by
   $β = \frac{λD}{d}$

i.e.,    $λ = \frac{βd}{D}$
$\Rightarrow$ $λ = \frac{1.5 \times 10^{- 3} \times 0.3 \times 10^{- 3}}{0.75} = 6000 \times 10^{- 10} m = 6000 Å$

(a) Fringe width is given by, $β = \frac{λD}{d}$ .

when D is doubled, fringe width $β$ is also doubled.

i.e., $β = 1.5 \times 2 = 3.0 mm$

(b) When d is doubled, $β$ is reduced to half.

i.e.,     $β = \frac{1.5}{2} = 0.75 mm .$

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