A light ray between two parallel mirrors
A light ray between two parallel mirrors
IP 1
7 marks
Two plane mirrors are parallel and face each other. A ray of light \(SP\) meets mirror 1 at \(P\), making an angle \(x\) with the mirror, reflects to \(Q\) on mirror 2, and reflects again along \(QR\). Model the reflections with the law of reflection: at each mirror the ray leaves at the same angle to the mirror as it arrives, on the other side of the normal.
- Explain why \(PQ\) makes an angle \(x\) with mirror 1 and an angle \(x\) with mirror 2.[2]
- Hence show that \(QR\) is parallel to \(SP\).[3]
- For \(x=35^\circ\), find the angle \(\angle SPQ\).[1]
- State which assumption about the mirrors is needed for part (b) to hold.[1]
Solution:
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Answer:(a) law of reflection at \(P\); alternate angles between the parallel mirrors at \(Q\) (b) \(SP\) and \(QR\) both make angle \(x\) with parallel mirrors in the same direction, so \(QR\parallel SP\) (c) \(110^\circ\) (d) the mirrors are exactly parallel
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