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University of Wisconsin - Milwaukee

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Problem 46 Hard Difficulty

Two stars located 23 light-years from Earth are barely resolved using a reflecting telescope having a mirror of diameter 68 $\mathrm{cm} .$ Assuming $\lambda=575 \mathrm{nm}$ and assuming that the resolution is limited only by diffraction, find the separation between the stars.

Answer

2.24 \times 10^{11} m

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Video Transcript

So in this problem we have the distance between the stars and Earth is 23 light years. But one light, eerie calls 9.461 times 10 to the 15 meter. So that means the distance between the Earth and the stars is going to be 23 times 9.461 times 10 to the 15 meter. The mirror diameter of the reflecting Telescope is 68 centimeter. The web link of the light that is used to do the observation is 575 nanometer. Now, assuming that the two stars air just result, we want to find the separation between the stars. So the first thing that we want to do is we want to find out the angular separation between the stars. So in that case, angular separation Terra is going to be s over our right. However, when the two objects air just resolved, data is going to be approximately approximately cold out there. I mean, which is yes, over, huh? And you know when we're using the reflecting telescope with circular aperture diameter, mirror diameter, that Mrs they're mean is going to be called the 1.22 times were blanked over D. So from here we can see that s is going to be 1.2 to Lambda over the so Rhys of this is pretty straightforward. All we have to do is 1.22 times. Sorry I'm missing are here 1.22 times the World Bank of Light, which is 5 75 times 10 to the negative. Nine times the distance of 23 light years, which is 23 times 9.461 times 10 to the negative. It's 10 to the positive 15 all right over the diameter, which is 0.68 and this is going to give us 2.2 times tend to the 11 meter

University of Wisconsin - Milwaukee
Top Physics 103 Educators
Christina K.

Rutgers, The State University of New Jersey

Andy C.

University of Michigan - Ann Arbor

Aspen F.

University of Sheffield

Jared E.

University of Winnipeg