1) Size of the image: 2 cm
In order to calculate the size of the image, we can use the following proportion:
[tex]p:q = h_o : h_i[/tex]
where
p = 80 m is the distance of the tree from the pinhole
q = 20 cm = 0.2 m is the distance of the image from the pinhole
[tex]h_o[/tex] = 8 m is the heigth of the object
[tex]h_i[/tex] is the height of the image
By re-arranging the proportion, we find
[tex]h_i = \frac{h_o \cdot q}{p}=\frac{(8 m)(0.2 m)}{80 m}=0.02 m=2 cm[/tex]
2) Magnification: 0.0025
The magnification of a camera is given by the ratio between the size of the image and the size of the real object:
[tex]M=\frac{h_i}{h_o}[/tex]
so, in this problem we have
[tex]M=\frac{0.02 m}{8 m}=0.0025[/tex]
