The figure shows a modified Young’s double slit experimental set-up. Here SS_{2}-SS_{1}=\lambda /4

(a) Write the condition for constructive interference.
(b) Obtain an expression for the fringe width.

 

 
 
 
 
 

Answers (1)
S safeer

(a) The path difference;

S_{2}P-S_{1}P=(\frac{y_{n}d}{D}+\frac{\lambda }{4})

 for constructive inference; the path difference =n\lambda

n\lambda=(\frac{y_{n}d}{D}+\frac{\lambda }{4})

where, n=0,1,2,3,.........

(b) The position of nth bright fringe

\frac{y_{n}d}{D}={n\lambda}-\frac{\lambda}{4}

y_n=(n-\frac{1}{4})\frac{\lambda D}{d}

\therefore Fringe width  \beta =y_{n}-y_{n-1}

\beta=(n-\frac{1}{4}-(n-1-\frac{1}{4}))\frac{\lambda D}{d}

\beta =\frac{\lambda D}{d}

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