Question

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Derive an expression for the deviation formed by the combination of two plane mirrors.​

Answer 1

We want to determine the angle of deviation for a plane mirror.

Let the angle of incidence be (in degrees) θ.

⇒ The angle of reflection is also θ.

⇒ The angle that the reflected ray makes with the mirror is 90o−θ.

⇒ The angle that the path of the incident ray would have made with the mirror had it passed through the mirror without getting either reflected or refracted is also 90o−θ.

⇒ The angle between the reflected ray and the path of the incident ray if it passed through the mirror without getting either reflected or refracted is 2(90o−θ)=180o−2θ.

But this angle is angle by which the ray of light has got deviated.

⇒ The angle of deviation for a plane mirror is 2(90o−θ)=180o−2θ.

See the following link for a specific case and a figure

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