In free space (\"vacuum\"), where the net charge and current flow is zero, the s
ID: 1459092 • Letter: I
Question
In free space ("vacuum"), where the net charge and current flow is zero, the speed of an EM wave is given by v=1/00. If, instead, an EM wave travels in a nonconducting ("dielectric") material with dielectric constant K, thenv=1/K00. For frequencies corresponding to the visible spectrum (near 5×1014Hz), the dielectric constant of ice is 1.72.
Predict the speed of light in ice.
I put 2.3(10^8)m/s, and 1.74(10^8)m/s but it is wrong
Compare this value (as a percentage) with the speed of light in a vacuum.
I put 43.8%, but it is wrong
I have only one chance for each question. Could you guys help me out?
Explanation / Answer
Speed of light in vacuum, c = 1/(oo)1/2 = 1/[(8.854 * 10-12) * (4 * 10-7)]1/2 = 2.998 * 108 m/s
Speed of light in ice, vice = 1/(Koo)1/2 = 1/[(1.72 * (8.854 * 10-12) * (4 * 10-7)]1/2 = 2.286 * 108 m/s
Now, (vice/c) * 100 = 100/(K)1/2 = 100 / 1.721/2 = 76.25 %
So, speed of light in ice is 76.25% of speed of light in vacuum.