A student investigates reflections in a plane mirror. A ray-trace sheet is shown in Fig. 3.1. Fig. 3.1 The student views the images of pins $$\(P_{1}\)$$ and $$\(P_{2}\)$$ from the direction indicated by the eye in Fig. 3.1. He places two pins, $$\(P_{3}\)$$ and $$\(P_{4}\)$$, so that pins $$\(P_{3}\)$$ and $$\(P_{4}\)$$ and the images of $$\(P_{2}\)$$ and $$\(P_{1}\)$$ all appear exactly one behind the other. The positions of $$\(\mathrm{P}_{3}\)$$ and $$\(\mathrm{P}_{4}\)$$ are shown on Fig. 3.1. (i) Draw a line through the positions of $$\(\mathrm{P}_{3}\)$$ and $$\(\mathrm{P}_{4}\)$$. Continue the line until it meets $$\(\mathbf{M} \boldsymbol{\mathrm { R }}\)$$. (ii) Measure the acute angle $$\(\alpha\)$$ between this line and the horizontal line MR. An acute angle is an angle less than $$\(90^{\circ}\)$$. $$\[ \alpha= \]$$

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