You use a lens of diameter D and light of wavelength λ and frequency f to form an image of two closely spaced and distant objects. Which of the following will increase the resolving power? (a) Use a lens with a smaller diameter; (b) use light of higher frequency; (c) use light of longer wavelength. In each case justify your answer.
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You use a lens of diameter D and light of wavelength λ and frequency f to form an image of two closely spaced and distant objects. Which of the following will increase the resolving power? (a) Use a lens with a smaller diameter; (b) use light of higher frequency; (c) use light of longer wavelength. In each case justify your answer.
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- Two motorcycles separated laterally by 2.30 m are approaching an observer wearing night-vision goggles sensitive to infrared light of wavelength 885 nm. (a) Assume the light propagates through perfectly steady and uniform air. What aperture diameter is required if the motorcycles’ headlights are to be resolved at a distance of 12.0 km? (b) Comment on how realistic the assumption in part (a) is.Diameter of the objective lens of a telescope is 250 cm. For light of wavelength 600 nm coming from a distant object, the limit of resolution of the telescope is close to what value?The Hubble Space Telescope (HST) orbits Earth at an altitude of 613 km. It has an objective mirror that is 2.40 m in diameter. If the HST were to look down on Earth's surface (rather than up at the stars), what is the minimum separation of two objects that could be resolved using 549 nm light? [IVote: The HST is used only for astronomical work, but a (classified) number of similar telescopes are in orbit for spy purposes.]
- Yellow light of wavelength 580 nm is used to view an object under a microscope. The objective lens diameter is 9.15 mm. (a) What is the limiting angle of resolution? prad (b) Suppose it is possible to use visible light of any wavelength. What color should you choose to give the smallest possible angle of resolution, and what is this angle? color ---Select--- angle prad (c) Suppose water fills the space between the object and the objective. What effect does this change have on the resolving power when 580-nm light is used? effect ---Select--- minimum resolvable angle pradShow that a plano-convex lens with a spherical refractive surface of radius R and diameter D forms a perfect image of an infinitely distant point at its focus for 1 R n 4√ √2(n-1)³ Hint: apply Rayleigh's 1/4 wave of optical path difference criterion. (f-number) 2 >Find the minimum telescope aperture that could resolve an object with angular diameter 0.35 arcsecond, observed at 520-nm wave- length. (Note: 1 arcsec = 1/3600°.)
- Consider a telescope on Earth that aims to distinguish (solve) two points over the moon separated by a distance of 1.7 km when the moon is at a distance of 3.8x105 km. By the Rayleigh resolution criterion, what is the minimum diameter of the opening of this telescope? Consider the wavelength equal to 0.55 µm. 21 cm 12 cm 25 cm 15 cm 18 cmYou use a lens of diameter D and light of wavelength l and frequency f to form an image of two closely spaced and distant objects. Which of the following will increase the resolving power? (a) Use a lens with a smaller diameter; (b) use light of higher frequency; (c) use light of longer wavelength. In each case justify your answer.(a) How far from some grains of red sand must you be so that you are just at the limit of resolving the grains if your pupil diameter is 3mm, the grains are spherical with radius 50μm, and the light from the gains has wavelength 650nm? (b) If the grains were blue and the light from them had wavelength 400nm instead, would the answer to (a) be larger or smaller? (c) Now let's say you are a superhero and you had x-ray vision, so you could see light that had a wavelength of 0.1nm instead. Now how far could you be from the gains of sand to just be at the limit to distinguish one grain of sand from another? (with the same pupil diameter). (assume you're on the beach and there's plenty of light from many frequencies bouncing off the sand, and when you turn on your x-ray vision you aren't bothered by all the other frequencies around).
- Find the separation of two points on the Moon’s surface that can just be resolved by the 200 in. (= 5.1 m) telescope at Mount Palomar, assuming that this separation is determined by diffraction effects. The distance from Earth to the Moon is 3.8* 10^5 km.Assume a wavelength of 550 nm for the lightIn a biprism experiment, when a convex lens was placed between the biprism and eyepiece at a distance of 30 cm from the slit, the virtual images of the slits are found to be separated by 7 mm. If the distance between the slit and biprism is 10 cm and between the biprism and eyepiece is 80 cm, find the linear magnification of the image.An amateur astronomer wants to build a telescope with a diffraction limit that will allow him to see if there are people on the moons of Jupiter. (a) What diameter mirror is needed to be able to see 1.00 m detail on a Jovian Moon at a distance of 7.50×108 km from Earth? The wavelength of light averages 600 nm. (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?