Solved Problem on Propagation of Light
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A cup of 12 cm high is placed in front camera obscura at 2 m from the hole. The distance from the hole to the opposite wall is 30 cm. Calculate the height of the image projected on the wall.


Problem data:
  • Object height:    y = 12 cm;
  • Object distance:    p = 2 m;
  • Camera length:    q = 30 cm.
Problem diagram:

Figure 1

Solution

First, we must convert the distance from the object to the camera given in meters (m) to centimeters (cm), rather than converting all other units to meters as usual.
\[ p=2\;\text{m}=2\times (100\;\text{cm})=200\;\text{cm} \]
The height of the image is given by
\[ \bbox[#99CCFF,10px] {\frac{y'}{y}=\frac{q}{p}} \]
\[ \begin{gather} \frac{y'}{12}=\frac{30}{200}\\ y'=\frac{30\times 12}{200}\\ y'=\frac{360}{200} \end{gather} \]
\[ \bbox[#FFCCCC,10px] {y'=1,8\;\text{cm}} \]
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