Using Young's double slit experiment, a monochromatic light of wavelength $5000 Å$ produces fringes of fringe width $0.5 m m$ . If another monochromatic light of wavelength $6000 Å$ is used and the separation between the slits is doubled, then the new fringe width will be:
$0.3 m m$
$0.6 m m$
$1.0 m m$
$0.5 m m$

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Solution

The correct option is A $0.3 m m$
Fringe width $= \frac{λ D}{d}$

when light of $5000$ Å is used;

$0.5 = \frac{5000 D}{d}$

$\Rightarrow \frac{D}{d} = \frac{0.5}{5000}$

when light of $6000$ Å is used and separation between slits is doubled;

$β^{'} = \frac{6000}{2} \times \frac{D}{d}$

$β^{'} = \frac{6000}{2} \times \frac{0.5}{5000}$

$\Rightarrow β^{'} = \frac{3}{10} = 0.3 m m$

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