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

at theta =0 I =Im (sin 0/0)^2 which is undefined as 0/0 is undefined so sin(0/0) is also undefined...

2) as theta -> 0 sin theta -> 0

so I = Im (sin(R*theta)/R*theta)^2 = Im (R*theta/R *theta)^2 = Im ...i used above fact twice while solving this

Related Questions

Navigate

• Browse (All)
• Browse L
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.