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Yellow light (lambda=6000Å) illuminates ...

Yellow light (`lambda=6000Å`) illuminates a single slit of width `1xx10^(-4)m`. Calculate : (i) the distance between the two dark lines on either side of the central maximum, when the diffraction pattern is viewed on a screen kept `1.5m` away from the slit, `(ii)` the angular spread of the first diffraction minimum.

Text Solution

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(i) Here, `lambad=6000Å=6xx10^(-7)m`
`a=1xx10^(-4)m`, `D=1.5m`
Angular separation of two dark bands on each side of central bright band,
`2theta=(2lambda)/(a)`
and actual distance between them,
`2x=(2lambda)/(a)xxD`
`=(2xx6xx10^(-7)xx1.5)/(1xx10^(-4))`
`=1.8xx10^(-2)m`
`(ii)` For first minimum, `(sintheta~~theta)`
`theta=(lambda)/(a)=(6xx10^(-7))/(1xx10^(-4))`
`=6xx10^(-3)` rad.
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