Light waves of frequency (Lambda %u03BB) passing through a slit of width produce

Question

Light waves of frequency (Lambda %u03BB) passing through a slit of width produce a Fraunhofer diffraction pattern of light and dark fringes . The intensity as a function of the angle (theta) is given by

I(theta)= Im(sin(Rsin(theta)/Rsin(theta) all squared

Where R= (%u03C0)(a)/%u03BB and is a constant.

The qusetion is ...

1- Show that the intensity function is not defined at (theta) =0.

2- Check numerically that I(theta ) approaches Im as (theta) -->0 for any two values of R (e.g., Choose two integer values).

This link has the picture of the Fraunhofer diffraction pattern graph.

http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/fraungeo.html

Explanation / Answer

1st the function IS defined for theta = let u = Rsin[theta] then u have [sin[u]/u] as theyta --> 0 u--->0 and sin u/u ---> 1

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