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$\bullet$$\bullet$ Spy satellites? Rumor has it that the U.S. military has spysatellites in orbit carrying telescopes that can resolve objectson the ground as small as the width of a car's license plate. Ifwe assume that such satellites orbit about 400 $\mathrm{km}$ above theground (which is typical for orbiting telescopes) and that theyfocus light of wavelength $500 \mathrm{nm},$ what would have to be theminimum diameter of the mirror (or objective lens) of thiskind of a telescope in order to resolve such small objects?(Measure the width of a car's license plate.)

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$=80 \mathrm{~cm}$

Physics 102 Electricity and Magnetism

Physics 103

Chapter 26

Interference and Diffraction

Electromagnetic Waves

Reflection and Refraction of Light

University of Michigan - Ann Arbor

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Lectures

02:30

In optics, ray optics is a geometric optics method that uses ray tracing to model the propagation of light through an optical system. As in all geometric optics methods, the ray optics model assumes that light travels in straight lines and that the index of refraction of the optical material remains constant throughout the system.

10:00

In optics, reflection is the change in direction of a wavefront at an interface between two different media so that the wavefront returns into the medium from which it originated. Common examples include the reflection of light, sound and water waves. The law of reflection says that for specular reflection the angle at which the wave is incident on the surface equals the angle at which it is reflected. Reflection may also be referred to as "mirror image" or "specular reflection". Refraction is the change in direction of a wave due to a change in its speed. The refractive index of a material is a measure of its ability to change the direction of a wave. A material with a higher refractive index will change the direction of a wave to a greater degree than a material with a lower refractive index. When a wave crosses the boundary between two materials with different refractive indices, part of the wave is refracted; that is, it changes direction. The ratio of the speeds of propagation of the two waves determines the angle of refraction, which is the angle between the direction of the incident and the refractive rays.

02:17

Assume that a spy satellit…

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Photographic cameras on sp…

01:13

A spy satellite is orbitin…

04:51

The telescopes on some com…

07:52

The Hubble Space Telescope…

01:23

A spy satellite uses a tel…

04:45

01:08

09:11

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A spy satellite orbiting …

all right. Rumor has it we have super secret spy satellites in orbit carrying telescopes that can look at a car's license plate. So let's see how reasonable this is. So assuming that our super secret satellite is a distance well 400 kilometers away and we're observing light that 508 meters wavelength, what diameter does that observation lens have to be in order to see clearly things the size of a license plate? So we go on Google and look up the length of a license plate about 12 inches, which is 30.48 centimeters. So it's the value we're going to use for this because it just says measure license plate and I don't want to go outside causes coach. All right, so if you look at our Railly angle again, that tells us the minimum resolution angle for looking at stuff. That's our 1.22 Landa over tea. It's definitely safe to assume that our satellites are much, much, much further away than the size of a license plate. So this approximation that Saito's why over s definitely holds. So if I stick those two things together, whatever s and now we're solving for D. So move my I d to the other side. Move us over here and move. Why? Down here? So D is equal to 1.2 to Lambda s over. Why? If I plug in my numbers? Lambo was 500 Nano meters s waas the distance of my satellite. So 400 kilometers 10 to 3 over. Why? Just 30.48 times 10 to the negative too. Leaders gives me a year a diameter of a lens of approximately 80 scent of years, which is a totally reasonable size to put on a telescope that's floating around us in space on a satellite so think we might actually have some super secret spy satellites?

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