The QCC Observatory has a 16-inch diameter telescope with a digital recorder. A

Question

The QCC Observatory has a 16-inch diameter telescope with a digital recorder. A ring structure object was recorded as having 300 pixels in diameter at 5500+10X nm at a resolution of 2.5 pixels. The ring center had a un-resolvable core with a surrounding of several progressively fainter secondary rings. A NASA database search showed such an object ABCDEF at 4+2Xmillion light years away. Find the object diameter in kilometer and light year. Find the diameter of the second circular maxima at the ABCDEF center in pixels when using the diffraction profile of a single slit as an approximation Find the luminosity in J/s of ABCDEF when the detected brightness was 3 nano-watt using the inverse-square law in sound energy propagation. Write assumptions when used.

Explanation / Answer

a) To find diameter

W. K.T

1 pixel = 2.6458 x 10-7 kilometer

so for a diameter of 300 pixel = 7.9374*10^-5 km

1 Km = 1.057 * 10^-13 light years

For  7.9374*10^-5 km = 8.38*10^-18 light years.

b)

Let y be the distance from the center of the central diffraction maximum to the first diffraction minimum.

The angle T is related to this distance y and the distance to the screen, L, by the equation:

tan T = y / L

Since the angle T is very small, cos T » 1. Thus, tan T » sin T. Then, combining the above equation with equation (*), we have sin T = l / a » y / L, or

y = L l / a

And so, given the distance to the screen, the width of the slit, and the wavelength of the light, we can use the equation y = L l / a to calculate where the first diffraction minimum will occur in the single slit diffraction pattern. And we have learned that this is the point where the waves from point sources in the slit all cancel in pairs that are out of phase.

Where, I is the wavelength

L is the distance between the screen and the slit.

a is the slit width

T is the angle.

Plug in all the values and you will get the required results.

c) w.k.t

b = L/4 pi (d^2)

L = 3*10^-9*4*pi*(4+2x)^2 j/sec.

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