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A Parallel beam of light of 500 nm falls...

A Parallel beam of light of 500 nm falls on a narrow slit and be resulting diffraction pattern is observed on a screen 1 m away. It is observed that the first minimum is at a distance of 2.5 mm from the centre of the screen. Calculate the width of the slit.

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Formula : From condition of diffraction,
` a sin theta = n lamda ` (for minima)
` = (n+ 1/2) lamda ` (for minima)`

Provided n = 1, 2, 3 ... and n = 0 for central maximam
From condition of minima,
` a sin theta = lamda (n= 1)`
Since the value of is of nm, so
`a.theta = lamda rArr a.lamda/D lamda " " [ " angle =( "arc")/"("radius")`
` a = (lamda D)/(y) = (500 xx 10^(-9) xx 1)/(2.5 xx 10^(-3)) m`
` = 2 xx 10^(-4) m`
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