Two plane mirror AB and AC are inclined at an angle $θ = 2 0^{\circ}$ . A ray of light starting from point P is incident at point Q on the mirror AB, then at R on mirror AC and again on S on AB finally the ray ST goes parallel to mirror AC. The angle $i$ which the ray makes with the normal at point Q on mirror AB is

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TestHub · Accepted Answer

Reverse the ray from T.

A mirror along angle $α$ changes direction $ϕ$ to $2 α - ϕ$ .

Take AC along 0° and AB along 20°.

Reversed ray along TS: $ϕ = 18 0^{\circ}$ .

Reflect at S (AB): $2 (2 0^{\circ}) - 18 0^{\circ} = - 14 0^{\circ}$ .

Reflect at R (AC): $0 - (- 14 0^{\circ}) = 14 0^{\circ}$ .

Reflect at Q (AB): $4 0^{\circ} - 14 0^{\circ} = - 10 0^{\circ}$ .

Normal to AB is along $- 7 0^{\circ}$ , so $i = - 7 0^{\circ} - (- 10 0^{\circ}) = 3 0^{\circ}$ .

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