Oona reads that water's index of refraction is 1.33. No speed is listed. She wants the speed of light in water.
This lesson runs the index equation the other way: from n to the speed in the medium. Then the drill mixes both directions.
The givens now are c = 3.00 × 10⁸ m/s and the index, n = 1.33. The unknown is v.
The equation is still the same one: n = c/v. There is no second formula to learn.
Rearrange it for v: multiply both sides by v, then divide both sides by n. That gives v = c ÷ n.
Divide: 3.00 ÷ 1.33 = 2.26, and the 10⁸ rides along. The speed of light in water is 2.26 × 10⁸ m/s.
Check the size: a medium speed must come out BELOW 3.00 × 10⁸ m/s, because n is greater than 1. 2.26 × 10⁸ m/s passes.
Water's index of refraction is 1.33. Calculate the speed of light in water.
Write down the values:
c = 3.00 × 10⁸ m/s, n = 1.33, v = ?
Write down the equation, and rearrange for v:
n = c/v, so v = c ÷ n
Substitute in the values, and calculate:
3.00 ÷ 1.33 = 2.26, and the 10⁸ rides along, so v = 2.26 × 10⁸ m/s.
The speed of light in water is 2.26 × 10⁸ m/s.
Sapphire's index of refraction is 1.77. Calculate the speed of light in sapphire, to three significant figures.
Write down the values:
c = 3.00 × 10⁸ m/s, n = 1.77, v = ?
Write down the equation, and rearrange for v:
n = c/v, so v = c ÷ n
Substitute in the values, and calculate:
3.00 ÷ 1.77 = 1.69, and the 10⁸ rides along, so v = 1.69 × 10⁸ m/s.
The speed of light in sapphire is 1.69 × 10⁸ m/s.
Window glass has an index of refraction of 1.52. Calculate the speed of light in the glass, in m/s, to three significant figures.
Light travels at 2.21 × 10⁸ m/s in ethanol. Calculate ethanol's index of refraction, to two decimal places. Answers within 0.03 are accepted.
Ice has an index of refraction of 1.31. Calculate the speed of light in ice, in m/s, to three significant figures.
Cubic zirconia has an index of refraction of 2.16. Calculate the speed of light in it, in m/s, to three significant figures.
Light travels at 1.89 × 10⁸ m/s in polycarbonate, the plastic in shatterproof glasses. Calculate its index of refraction, to two decimal places. Answers within 0.03 are accepted.
Light travels at 2.17 × 10⁸ m/s in rubbing alcohol. Calculate its index of refraction, to two decimal places. Answers within 0.03 are accepted.
Quartz has an index of refraction of 1.46. Calculate the speed of light in quartz, in m/s, to three significant figures.
Light travels at 2.08 × 10⁸ m/s in a clear resin. Calculate the resin's index of refraction, to two decimal places. Answers within 0.03 are accepted.
Nilo calculates the speed of light inside a glass block and gets 4.5 × 10⁸ m/s. Which check shows the answer must be wrong, before any recalculation?