Question

a) Light of wavelength 585 nm passes through a slit 6.00 × 10^-6 m wide and falls on a screen that is 2.28 m away. What is the distance on the screen from the center of the central bright fringe to the third dark fringe on either side? b) Two stars are 4.7 × 10^11 m apart and are equally distant from the earth. A telescope has an objective lens with a diameter of 1.06 m and just detects these stars as separate objects. Assume that light of wavelength 580 nm is being observed. Also, assume that diffraction effects, rather than atmospheric turbulence, limit the resolving power of the telescope. Find the maximum distance that these stars could be from the earth.

          a) Light of wavelength 585 nm passes through a slit 6.00 × 10^-6 m wide and falls on a screen that is 2.28 m away. What is the distance on the screen from the center of the central bright fringe to the third dark fringe on either side?
b) Two stars are 4.7 × 10^11 m apart and are equally distant from the earth. A telescope has an objective lens with a diameter of 1.06 m and just detects these stars as separate objects. Assume that light of wavelength 580 nm is being observed. Also, assume that diffraction effects, rather than atmospheric turbulence, limit the resolving power of the telescope. Find the maximum distance that these stars could be from the earth.

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University Physics with Modern Physics

Hugh D. Young 14th Edition

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Solved by Expert Sam Stansfield

06/11/2022

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We are asked to find the distance on the screen from the center of the central bright fringe to the third dark fringe on either side. Using the formula \(X = \frac{D \cdot M \cdot \lambda}{a}\), where \(X\) is the distance on the screen, \(D\) is the distance to Show more…

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a) Light of wavelength 585 nm passes through a slit 6.00 × 10^-6 m wide and falls on a screen that is 2.28 m away. What is the distance on the screen from the center of the central bright fringe to the third dark fringe on either side? b) Two stars are 4.7 × 10^11 m apart and are equally distant from the earth. A telescope has an objective lens with a diameter of 1.06 m and just detects these stars as separate objects. Assume that light of wavelength 580 nm is being observed. Also, assume that diffraction effects, rather than atmospheric turbulence, limit the resolving power of the telescope. Find the maximum distance that these stars could be from the earth.

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Transcript

00:01 This problem is about diffraction.

00:04 We have two different kinds of diffraction problems, one with a single slit and one with a circular opening.

00:10 We'll do the single slit one first.

00:15 So we're asked to find x.

00:18 We're given that we have a single slit with width a.

00:22 We know our wavelength.

00:24 And we want to find out what x is when we know that m equals 3 for our order number.

00:34 Okay, so our formula is that m lambda is equal to a sine theta for a minimum.

00:49 That's what we're looking for.

00:52 And one thing we know from looking at the diagram is that we can use sine theta is equal to x over capital d.

01:03 We can do that because we know the angle is small.

01:08 So ultimately we want to find x.

01:11 We get a formula that looks like this.

01:14 M -lamda is a -x over d.

01:18 We can solve that for x is d -m -a.

01:28 And when i substitute all my numbers in, i find out that x is 0 .667.

01:40 And that gives us part a.

01:45 And now part b, we have a star or a pair of stars that are pretty far away.

01:56 And we know the distance between them is given as 4 .7 times 10 to the 11 meters.

02:12 And we're also told that when our telescope diameter is exactly 1 .06...

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