 Solution

ID: past-exam-of-the-optics-and-electrodynamics-course-of-the-university-of-cambridge/2016/paper-1/1/a/solution

Interpreting the cone as Cherenkov radiation, its angle gives the speed, not directly the mass:

cos θ = \frac{c}{n v} = \frac{1}{n β}, γ = (1 - \frac{1}{n ^{2} c o s ^{2} θ})^{- 1/2} .

Combining this with the relativistic kinetic energy

T = (γ - 1) m c^{2}

m = \frac{T}{c ^{2} [ ( 1 - \frac{1}{n ^{2} c o s ^{2} θ} ) ^{- 1/2} - 1 ]} .

The material must be transparent at the observed frequency,

n

n cos θ > 1

. For

T > 0

this requires

0 < θ < arccos (1/ n)

for a massive particle above threshold. Radiation of an unspecified other origin would not determine the mass from these data alone.

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