Two slits spaced 0.25 mm apart are placed at 0.75 m from a screen and illuminate

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Two slits spaced 0.25 mm apart are placed at 0.75 m from a screen and illuminated by coherent light with a wavelength of 650 nm. The intensity at the centre of the central maximum

(θ = 0^{\circ})

is

I_{0}

. The distance on the screen from the centre of central maximum to the point where the intensity has fallen to

\frac{I_{0}}{2}

is nearly

Options:

A . 0.1 mm

B . 25 mm

C . 0.4 mm

D . 0.5 mm

Answer: Option D
:
D

I = I_{0} c o s^{2} \frac{(π d s i n θ)}{λ} = \frac{I_{0}}{2}

c o s (\frac{π d s i n θ}{λ}) = \frac{1}{\sqrt{2}}

we get,

x = \frac{λ D}{4 d} = \frac{650 \times 10^{- 9} \times 0.75}{4 \times 0.25 \times 10^{- 3}} = 487.5 \times 10^{- 6} m

= 0.4875 m m = 0.5 m m

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