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Mathematics course of the University of Cambridge

Past exam of the mathematics course of the University of Cambridge

2022

Paper 4

For a photon,
$$
\mathbf u=c(\cos\theta,\sin\theta,0).
$$
Part (ii) gives the first-order changes
$$
\delta u_x=-V\sin^2\theta,
\qquad
\delta u_y=V\sin\theta\cos\theta.
$$
For a vector of fixed leading-order magnitude $c$, its small change of angle is
$$
\delta\theta
=\frac{u_x\delta u_y-u_y\delta u_x}{c^2}.
$$
Substitution yields the <relativistic aberration> formula
$$
\boxed{\theta'-\theta=\frac Vc\sin\theta}
$$
to leading order.

Solution

Past exam of the mathematics course of the University of Cambridge / 2022 / ia / Paper 4 / 12C / b / iii / Solution

Past exam of the mathematics course of the University of Cambridge / 2022 / ia / Paper 4 / 12C / b / iii / Solution

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