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  4. Two slits are one millimeter apart and the screen is placed one metre away. The wavelength of light used is 500 nm What should be the width of each slit to obtain 10 maxima of the double-slit pattern within the central maxima of the single slit pattern.

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Q. Two slits are one millimeter apart and the screen is placed one metre away. The wavelength of light used is 500 nm What should be the width of each slit to obtain 10 maxima of the double-slit pattern within the central maxima of the single slit pattern.

Wave Optics

Solution:

Width of central maxima in diffraction $=\frac{2 D \lambda}{a}$
Width of 10 interference fringes $=10\left(\frac{D \lambda}{d}\right)$
$\Rightarrow \frac{10 D \lambda}{d}=\frac{2 D \lambda}{a}$
or $a=\frac{d}{5}=\frac{1\, mm }{5}=0.2\, mm$