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  1. Problems
  2. /A girl stands 2.8 m in front of a plane mirror…
EasyPhysicsHigh School (9–10)Optics › Reflection of LightNumericalBoard Exam

A girl stands 2.8 m in front of a plane mirror…

StemPy LabContributed by StemPy Lab

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

A girl stands 2.8 m2.8\ \text{m}2.8 m in front of a plane mirror. She walks toward it at 0.3 m/s0.3\ \text{m/s}0.3 m/s for 4 s4\ \text{s}4 s. How far is she from her image at the end? At what speed does she come closer to her image?

Check your answer

Work it out on paper, then type your number. The answer itself stays hidden.

m
m/s
Need a reminder? The key ideaShowHide

The angle of incidence equals the angle of reflection, both measured from the normal. A plane mirror gives a virtual, upright image of the same size, as far behind the mirror as the object is in front, with left and right swapped.

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

Step 1. The walk. In 4 s4\ \text{s}4 s she walks 0.3 m/s×4 s=1.2 m0.3\ \text{m/s} \times 4\ \text{s} = 1.2\ \text{m}0.3 m/s×4 s=1.2 m. She is now 2.8 m−1.2 m=1.6 m2.8\ \text{m} - 1.2\ \text{m} = 1.6\ \text{m}2.8 m−1.2 m=1.6 m from the mirror.

Step 2. The image. It is 1.6 m1.6\ \text{m}1.6 m behind the mirror, so she is 1.6 m+1.6 m=3.2 m1.6\ \text{m} + 1.6\ \text{m} = 3.2\ \text{m}1.6 m+1.6 m=3.2 m from it.

Step 3. The speed. Each second she gets 0.3 m0.3\ \text{m}0.3 m nearer the mirror, and so does the image from the other side. Together: 0.3 m/s+0.3 m/s=0.6 m/s0.3\ \text{m/s} + 0.3\ \text{m/s} = 0.6\ \text{m/s}0.3 m/s+0.3 m/s=0.6 m/s.

Answer: 3.2 m3.2\ \text{m}3.2 m, and 0.6 m/s0.6\ \text{m/s}0.6 m/s (twice her own speed).

Check. At the start the gap was 5.6 m5.6\ \text{m}5.6 m. It fell by 2.4 m2.4\ \text{m}2.4 m in 4 s4\ \text{s}4 s: 0.6 m/s0.6\ \text{m/s}0.6 m/s.

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  1. Reflection of light and the plane mirrorReflection and Mirrors

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