1.

When the frequency of the light used is changed from 4xx10^(14)s^(-1) to 5xx10^(14)s^(-1), the angular width of the principal (central) maximum in a single slit fraunhoffer diffraction pattern changes by 0.6 radian. What is the width of the slit (assume that the experiment is performed in vacuum) ?

Answer»

`1.5xx10^(-7)m`
`3xx10^(-7)m`
`5xx10^(-7)m`
`6XX10^(-7)m`

Solution :We know that fringe width of central MAXIMUM in Fraunhoffer diffraction, `beta_(0)=(2lamdaD)/(d)`
`therefore`Angular width of central maximum, `theta=(beta_(0))/(D)=(2lamda)/(d)`
On differentiating both sides, we GET
`Deltatheta=(2Deltalamda)/(d) implies d=(2Deltalamda)/(Deltatheta)`
Now, `Deltalamda=((c)/(upsilon_(1))-(c)/(upsilon_(2)))=(3xx10^(8))/(4xx10^(14))-(3xx10^(8))/(5xx10^(14))`
`=10^(-6)(0.75-0.6)=0.15xx10^(-6)=1.5xx10^(-7)m`
`therefore`Width of the slit, `d=(2xx1.5xx10^(-7))/(0.6)=5xx10^(-7)m`.


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