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CBSE Class 12-science Answered

Prove that the width of central maxima is twice the width of the secondary maxima. How does the width of central maxima depend on the width of the slit?
Asked by rajmishra.news | 27 Feb, 2019, 02:57: AM
answered-by-expert Expert Answer

In single slit experiment, central maximum intensity occurs when angle θ=0  and subsequent intensity maxima occurs
at θ = [ n+(1/2) ] λ, where n = ±1, ±2....etc

similarly minimum intensity occurs at θ = nλ ,where n = ±1, ±2....etc . This is illustrated in the above figure.
 
angular width of central maximum  is between θ = λ/a and θ = - λ/a . Hence width of central maximum = 2λ/a
 
angular width of  secondary maximum  is between θ = λ/a and θ = 2λ/a . Hence width of secondary maximum = λ/a
 
width of central maximum is inversly proportional to slit width a. If slit width is less,  central maximum width increases,
but intensity decreases if we reduce the slit width
Answered by Thiyagarajan K | 27 Feb, 2019, 04:38: PM

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