A jewellery shop owner has two identical clear gemstones but cannot remember which one is diamond and which one is rutile. Rutile is a clear gemstone that appears identical to a diamond. It is often used as a cheaper alternative to diamond in jewellery. She is aware that the refractive index of diamond is 2.4 and the refractive index of rutile is 2.9. She has a machine capable of measuring the speed of light through each material and basic measuring equipment. Briefly describe how the shop owner can distinguish between the diamond and rutile gemstones. Use calculations to support your answer.

To place a communications satellite into a geosynchronous orbit at an altitude of 22,240 mi above the surface of the earth, the satellite first is released from a space shuttle , which is in a circular orbit at an altitude of 185 mi, and then is propelled by an upper-stage booster to its final altitude. as the satellite passes through a, the booster's motor is fired to insert the satellite into an elliptic transfer orbit. the booster is again fired at b to insert the satellite into a geosynchronous orbit. knowing that the second firing increases the speed of the satellite by 4810ft/s, determine (a.) the speed of the satellite as it approaches b on the elliptic transfer orbit, (b.) the increase in speed resulting from the first firing at a.