To illustrate one of the ideas of holography in a simple way, consider a diffrac

Question

To illustrate one of the ideas of holography in a simple way, consider a diffraction grating with slit spacing d. The small-angle approximation is usually not valid for diffraction gratings, because d is only slightly larger than ?, but assume that the ?/d ratio of this grating is small enough to make the small-angle approximation valid.

Use the small-angle approximation to find an expression for the fringe spacing on a screen at distance L behind the grating. (Use any variable or symbol stated above as necessary.)

Explanation / Answer

sin(m) = m/d

small-angle approximation >>>> sin(m) = ym/L

>>>> ym = L sin(m)

>>>> ym = mL/d

>>>> the fringe spacing on a screen = L/d

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