Question

Obtain the formula of path difference at a point on the screen in Young's double slit experiment in
term of x d and D.​

Answer 1

Answer:

Consider the attachment,

Path difference = AP - BP   = $\\\tt n \lambda$   -------(i)

Now using geometry and diagram,

$\\\tt (AP)^{2} = D^{2} + (x+\dfrac{d}{2} )^{2}\\(BP)^{2} = D^{2} + (x-\dfrac{d}{2} )^{2}$

Then,

$\\\tt (AP)^{2} -(BP)^{2} = xd+ xd = 2xd\\AP -BP = \dfrac{2xd}{(AP+ BP)}$

For d<<D,

AP + BP = 2D

Using this value in equation above,

$\\\tt AP -BP = \dfrac{2xd}{(2D)} = \dfrac{xd}{D}$         ------------(ii)

Equating (i) and (ii)

$\\\tt n \lambda = \dfrac{xd}{D}$

Answer 2

Explanation:

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