a) Consider light from a helium-neon laser ( 632.8 nanometers)striking a pinhole

Question

a) Consider light from a helium-neon laser ( 632.8 nanometers)striking a pinhole with a diameter of 0.175mm . At what angle to the normal would the first dark ring be observed? b) Diffraction due to a circular aperture is important inastronomy. Since a telescope has a circular aperture of finitesize, stars are not imaged as points, but rather as diffractionpatterns. Two distinct points are said to be just resolved (i.e.,have the smallest separation for which you can confidently tellthat there are two points instead of just one) when the center ofone point's diffraction pattern is found in the first dark ring ofthe other point's diffraction pattern. This iscalled Rayleigh'scriterion for resolvability. Consider a telescope with an aperture of diameter 1.10 . d) What is the angular radius ofthe first dark ring for a point source being imaged by thistelescope? Use 550 nanometers for the wavelength, since this is near the average for visiblelight.

Explanation / Answer

Hello,

Here's the solution:

(a)

For such a case sin = m/d
Note that first dark fringe is observed for m = 1.22

Thus = sin-1 (m/d) = sin-1 (1.22x632.8x10-9/0.175x10-3)=0.252

(d)

Again the angular radius can be calculated as in part (a).

I hope that its 1.10 mm (convention ; since you did not specify)

Here   = sin-1 (m/d) = sin-1 (1.22x550x10-9/1.10 x 10-3) = 0.034

However if you are asking angular diameter as referred in http://en.wikipedia.org/wiki/Angular_diameter then you need to specify the distance D you are talking about.

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Hope this helps.

Please rate.

Cheers.

:)

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