Solved Problem on Propagation of Light
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On a sunny day, a building projects a shadow of 10 m in length at the same instant, a 5 m high pole projects a shadow of 2 m in length. Determine the height of the building.


Problem data:
  • Length of the shadow of the building:    D = 10 m;
  • Height of the post:    h = 5 m;
  • Lenght of the shadow of the post:    d = 2 m.
Problem diagram:

Let's consider that the rays of the sun are parallel (Figure 1).

Figure 1

Solution

Assuming that the rays from the Sun are parallel, we can say that the triangles ABC and A'B'C' are similar. From the Similarity of Triangles, we have
\[ \bbox[#99CCFF,10px] {\frac{H}{h}=\frac{D}{d}} \]
\[ \begin{gather} \frac{H}{5}=\frac{10}{2}\\ H=\frac{5\times 10}{2}\\ H=\frac{50}{2} \end{gather} \]
\[ \bbox[#FFCCCC,10px] {H=25\;\text{m}} \]
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