Fundamental Properties

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GRE Subject Test: Physics › Fundamental Properties

Questions 1 - 2

A monochromatic beam of $600\textup{ nm}$ light travels through a material with a phase velocity of $2*10^8\ \frac{\textup{m}}{\textup{s}}$ . What is the refractive index of the material?

Explanation

The phase velocity of light through a medium with refractive index is given by:

$v_p=\frac{c}{n}$

Solving this for and substituting our given value of :

$n=\frac{c}{v_p}=\frac{3\times10^8}{2\times10^8}=1.5$

A particle traveling through glass (index of refraction 1.33) emits Cherenkov radiation. Which of the following is a possible speed of the particle?

$\frac{7}{8}c$

$\frac{3}{8}c$

$\frac{1}{8}c$

$\frac{5}{8}c$

$\frac{9}{8}c$

Explanation

Cherenkov radiation is emitted by a particle traveling faster than the phase velocity of light in that medium. Because $n=\frac{4}{3}$ , the phase velocity of light in the glass is:

$v_p=\frac{c}{n}=\frac{3}{4}c$

This is the minimum velocity of a particle to be emitting Cherenkov radiation in glass. This eliminates all answers except $\frac{7}{8}c$ and $\frac{9}{8}c$ . The latter is impossible because it is greater than the speed of light in a vacuum, therefore the answer is $\frac{7}{8}c$ .

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