Mirror breaking the laws!

Electricity and Magnetism Level 4

Consider a spherical concave mirror of Radius of Curvature 5 c m 5 cm .

Consider a ray of light parallel to the principal axis at a distance of 2 c m 2 cm from it, strike the mirror and crosses the principal axis at a distance s s from the pole of the mirror.

Find s s (Approximately).

5.1cm 4.9 cm 4.8cm 5cm

Prakhar Gupta by Prakhar Gupta , 23, India

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1 solution

Prakhar Gupta
Jun 9, 2015

In Δ P M C \Delta PMC , sin ⁡ θ = 2 10 = 1 5 \sin\theta = \dfrac{2}{10} = \dfrac{1}{5} ⟹ cos ⁡ θ = 24 5 \implies \cos\theta = \dfrac{\sqrt{24}}{5} Now, applying sine rule in Δ P Q C \Delta PQC :- sin ⁡ θ C Q = sin ⁡ 2 θ C P \dfrac{\sin\theta}{CQ} = \dfrac{\sin2\theta}{CP} sin ⁡ θ 10 − s = 2 sin ⁡ θ cos ⁡ θ 10 \dfrac{\sin\theta}{10-s} = \dfrac{2\sin\theta\cos\theta}{10} 1 10 − s = cos ⁡ θ 5 \dfrac{1}{10-s} = \dfrac{\cos\theta}{5} 5 10 − s = 24 5 \dfrac{5}{10-s} = \dfrac{\sqrt{24}}{5} 10 − s 5 = 5 24 \dfrac{10-s}{5} = \dfrac{5}{\sqrt{24}} 10 − s = 25 24 10-s = \dfrac{25}{\sqrt{24}} s = 10 − 25 24 = 4.9 s = 10-\dfrac{25}{\sqrt{24}}=4.9

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Thank you for your problem. BTW I think it should be a Classical Mechanics problem.

Swapnil Das - 6 years ago

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Optics come under Electricity and magnetism. After all, light is an Electromagnetic wave.

Prakhar Gupta - 6 years ago

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