1- An object of height 5 cm is placed 30 cm in front of spherical concave mirror

Question

1- An object of height 5 cm is placed 30 cm in front of spherical concave mirror. If the image is real and 10 cm high, what is the radius of curvature of the mirror?

2- If you've ever flown, or been flown in, a twin-engine propeller-driven airplane, you know all about the irritating waaah-waaah-waaah sound thats heard whenever one engine is turning slightly faster than the other. Its so irritating that most high-end twins have a button labeled "auto-sync" the pilot presses it, and engine speeds are automatically matched, exactly. Explain, in as much technically accurate detail as you can, exactly where this irritating sound comes from. Feel free to include accounts of your personal experiences, or similar experiences (e.g., two band instruments playing out of tune) that are due to the same phenomenon.

3- This one may require a little web-crawling, although the title practically gives it away. Assume there are two planets in Earth's orbit; our own dear home, and a planet that's identical in every way except that it has no atmosphere (and therefore no life). Even though rotation rates are the same, the sun appears to set slightly earlier on the airless planet. (We're talking actual sunset times, not the length of twilight. Obviously, the airless planet wouldn't have a twilight. [Why?]) Explain the difference in sunset times.

4- Here's another one that will require a little web-crawling. Maxwell Equations describe electromagnetic radiation, which includes light, as perpendicular waves; an electrical field wave, and a magnetic field wave. We all know that electromagnetic radiation can travel through empty space. Otherwise, it would be awfully cold and dark here on Earth.So here's the question. Sound waves travel through air. Water waves travel through water. When a kid shakes a rope, waves travel down the rope. So, in the case of electromagnetic waves what the heck is doing the waving?

Explanation / Answer

u = -30 cm, i = 10 cm and O = 5 cm

m = i/o = 2.

so v = -60 cm

thus 1/u + 1/v = 2/R

-1/30 - 1/60 = 2/R

so R = -20 cm

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