 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/ii/paper-1/9e/b/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

Each photon loses a factor

(1 + z)^{- 1}

in energy, and cosmological time dilation reduces the photon arrival rate by another factor

(1 + z)^{- 1}

. Hence

L_{received} = \frac{L}{( 1 + z ) ^{2}},

n = 2

. The physical area of the sphere today is

4 πa (t_{0})^{2} x^{2}

F = \frac{L}{4 πa ( t _{0} ) ^{2} x ^{2} ( 1 + z ) ^{2}} .

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