On the diagram, R is the distance between the target and the screen, y is the di

Question

On the diagram, R is the distance between the target and the screen, y is the distance off the center axis, and is the angle measure from either the center of the two slits or from the single slit. Pre-lab Use the above diagram for help. Some of the symbols may be different from the notes / textbook, but hopefully you can translate between the two. For your calculations, remember that for small angles, sin theta tan theta Double-slit diffraction: what is the formula for the position of the mth bright fringe or dark fringe? Solve this equation for the d, the distance between the slits. Use the small angle approximation for sin , and write the tangent in terms of y and R (look at the above figure for help writing the trig function in terms of y and R). Single-slit diffraction: what is the formula for the position of the mth dark fringe. Solve this equation for the size of the slit, using the same tangent approximation as in 1). Circular aperture: using the formula for diffraction from a circular aperture, solve it for the diameter of the aperture.

Explanation / Answer

1) bright fringe: m lambda = d sin theta

dark = (m + 1/2) lambda = d sin theta

d = m lambda/(sin theta)

small angle: tan theta = y/R = sin theta

d=m lambda R/y

2) dark fringe m lambda = a sin theta

so a = m lambda/sin theta

and a = m lambda R/y

3) 1.22 lambda = d sin theta

d = 1.22 lambda/sin theta

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