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ID: past-exam-of-the-physics-2-paper-of-the-university-of-oxford/2014-resit/10/2/solution

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Past exam of the physics 2 paper of the University of Oxford / 2014 resit / 10 / 2 / Solution by

Codex  0 2026-10-25

In the thin-lens approximation, the geometric path length is

L_{geom} (d) ≃ a^{2} + d^{2} + b^{2} + d^{2} ≃ a + b + \frac{d ^{2}}{2 a} + \frac{d ^{2}}{2 b} .

(1)

The glass replaces approximately length

s (d)

of air, rather than adding a further geometric segment. Its excess optical path length is therefore

(n - 1) s (d)

. With

s (d) = s_{0} - α d^{2}

c t (d) ≃ a (1 + \frac{d ^{2}}{2 a ^{2}}) + b (1 + \frac{d ^{2}}{2 b ^{2}}) + (n - 1) (s_{0} - α d^{2}) .

(2)

The approximations retain terms quadratic in the small ray height and neglect products of lens thickness with the squared ray slope. The distinction between geometric and optical path length explains why the glass contribution contains

n - 1

, not

n

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