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$\bullet$ Two satellites at an altitude of 1200 $\mathrm{km}$ are separated by28 $\mathrm{km} .$ If they broadcast 3.6 $\mathrm{cm}$ microwaves, what minimumreceiving-dish diameter is needed to resolve (by Rayleigh'scriterion) the two transmissions?

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1.88 m

Physics 102 Electricity and Magnetism

Physics 103

Chapter 26

Interference and Diffraction

Electromagnetic Waves

Reflection and Refraction of Light

Cornell University

University of Washington

Simon Fraser University

McMaster University

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.

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Two satellites at an altit…

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A converging lens with a d…

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A spy satellite orbiting a…

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The radar system of a nav…

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Okay, So in this problem you have two satellites separated by a distance of 28 kilometers. Better distance 1200 commoners from the radio receiving dish. So if these were sending on the signal with a wavelength of 3.6 centimeters, what iss The diameter of the dish. So this is gonna be a situation or what is the diameter of the dish so that you can distinguish between these two signals? So it's just gonna be a case for a really angle. So theater really was given by 1.22 Lambda over D. And that's the minimum angle of separation between two things that you can distinguish them in your diffraction patterns. We also know that data is going to be small enough that we can approximate it. That's why over us. So why there's this distance between them and ass is the distance to the dish. So putting those two things together we have 1.2 to Lambda over D is equal to why over us. So if we saw for Dean, do you is he will too. 1.22 Landa, multiply my s over and divide by what So if I put those in 1.22 Lando's 3.6 centimeters. So it's 10 to the minus two meters s is the distance to the dish, let's or 1200 kilometers. So it's 1200 times 10 to the third. Need hers over. Why, which is our separation, which is 28 kilometers. So 20 attempts into the three meters here. So if I put that into my handy dandy calculator, the diameter of my dish was one point 88

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