Answer to Question #130847 in Optics for Great

Question

The sun is covered Buy a disc 2Cm diameter placed about 2m from the eye .if the distance from the pinhole to the screen is 50cm, find the length of the diameter of the suns image formed by the pinhole camera

Answer 1

Draw the figure:

What we have here is called similar triangles.

The similar triangles are the one with 2-cm base b_d and a height h_d of 2 m, and the other one with the sun as the base b_S and eye-sun distance h_S as the height:

$$\frac{b_S}{h_S}=\frac{b_d}{h_d}.$$

Now consider another pair of triangles: base b_i as image size and h_i = 50 cm, and the same triangle formed by the size of the sun as in the previous reasoning:

$$\frac{b_i}{h_i}=\frac{b_d}{h_d},\\\space\\ b_i=b_d\frac{h_i}{h_d}=2\frac{50}{200}=0.5\text{ cm}.$$

"Why didn't we take into account the fact that for the first triangle formed by the disk and eye the height of Sun triangle is 2 m greater?" - you might ask. The reason why we ignored this fact is that the distance to the sun is incredible and 2 m do not affect the final answer absolutely because 2 m are too small distance compared to the distance to the Sun.