Problem 171, Angular Resolution

Optical Telescopes and the Human Eyes

[superbeybladebattleburst]

My favorite teacher for ever you're just a legend despite of your age you are always working thanks a lot

[noobtextwritergamer]

going to sleep tommorow is exam of modern physics. and telling everyone because its 4 am and I dont know what I am doing

[gacserosaurus]

I was already typing my comment about the UV hahah thanks for the re-upload!

[koosjorritsma]

Hello dr Lewin, let me try, after looking at 8.02: ang.res (in vacuum) must be 1, 2*lambda/a = 0, 046 arc sec using 450 nm for blue. In practice, as you explained on earth: about 0, 5 to 1 arc sec. This answer comes close to the 1/25 arc sec you mention… groeten uit Nederland.

[surendrakverma]

Thanks Sir for posting important questions? Regards

[mdreugen]

(a) The maximum angular resolution for a telescope with an optical lens of 2.4m in diameter in monochromatic blue light (λ = 450nm) is approximately 0.05 arcseconds;
(b) The actual resolution for a ground based telescope with a lens of 2.4m in diameter is at its best 0.5 arcseconds (10 times lower than the maximum possible);
(c) The resolution of the Hubble Space Telescope (HST) for blue light matches the predicted maximum angular resolution of 0.05 arcseconds;
(d) The difference between a ground based telescope and HST is the Earth's atmosphere which by being in a constant movement (turbulent) it "blurs" the captured light, distorting the resolution more than 10 times;
(e) The James Web Telescope has a mirror of 6.5m in diameter. Its angular resolution for near IR (2µm) is approximately 0.08 arcseconds;
(f) If we consider the visible light at a wavelength of 500nm and a diameter of the pupil of 5mm than the angular resolution of the human eye is approximately 0.5 arcminutes.

Comments:
i. The angular resolution was evaluated using the following mathematical equation: θ = 1.22 * λ/a, where λ is the wavelength and a is the size of the lens/mirror (1.22 results from the geometry difference between a pinhole and a slit);
ii. The HST and JWST have approximately the same angular resolution, BUT the mirror of JWSP is approximately 2.7 times bigger than the lens of HST AND JWST "sees" in IR which is a much larger wavelength compared to the visible light captured by HST (4 times larger) and this is consistent with the calculations (the factor is 4/2.7 ≈ 1.5, thus 0.05 arcseconds * 1.5 ≈ 0.08 arcseconds).

[zacnutofficial]

Sir can you tell me what is the difference between uniform and constant??
Like uniform acceleration vs Constant acceleration ... are they can be used interchangeably

Plz sir Reply 💙❤🧡

[Hey_Ananyasingh]

He'll proffesor walter lewin i am ananya Kumari I read in class 10, those who try never give up 😊😊😊
I am see the lecture to another component and they kept to solve and here the line going to point your lecture and to line most to convert 😊😊

Thank for lecture 🙏🙏

[jayantachakraborty]

Hello sir, Need your blessings. Going to write JEE Advanced paper on 4th June ❤❤✨

[ulfhaller]

λ = 450-485 nm for blue light
D = 2.4 m
a) Max resolution = 1.22·λ/D [radians]
= (1.22·λ/D)·(180/ π) [degrees]
= (1.22·λ/D)·(180/ π)·3600 [arcsec]
≈ 0.05 arcsec.
b) 0.5 to 1 arcsec in best cases. (From your 8.02 lecture).
c) 0.05 arcsec
d) Turbulence in the atmosphere makes the picture blurry.
e) From Wikipedia the effective diameter of James Webb mirror is about 6.5 m.
λ = 2 µm and D = 6.5 m gives:
(1.22·λ/D)·(180/ π)·3600 ≈ 0.08 arcsec.
f) The pupil of the eye has about 3 – 5 mm, which gives a resolution of about
0.5 to 1 arcmin. (From your 8.02 lecture).

[Soham-Bhadra]

Solution : (a) Let D = Diameter of Mirror = 2.4 m, λ = wavelength of Blue Light = 4.5 ×〖 10〗^(-7) and θ = Maximum Angular Resolution . Now we know
θ = (1.22 λ)/D = (1.22)(4.5 × 10^(-7) ) /2.4 = 2.3 × 10^(-7) rad = 0.047 arcsec .
(b) We know that by turbulence in Earth’s Atmosphere the Angular Resolution of ground-based telescope is limited to about (.5) arcsec .

[duckyoutube]

You could do this problem in high school?!

No wonder you turned into a wizard.

[mdsahab]

Hallo hallo hallo Us Teacher I am Bangladesh