The screen of a pin-hole camera is a square, of side 0.16m and it is 0.15m behind the pin-hole. The camera is placed 11m from a flag staff is formed centrally on the screen. The image occupies three-quarters of the screen. What is the height of the flag staff?
To find the height of the flag staff, we need to use similar triangles and the concept of similar triangles. We know that the image formed on the screen is three-quarters the size of the actual object. Let's assume the height of the flag staff is "h".
Since the image formed on the screen is three-quarters the size of the actual object, the height of the image will be (3/4)h.
Now, we can form two similar triangles: one formed by the actual flag staff, and the other formed by the image on the screen.
In the similar triangles, the corresponding sides are proportional. The height of the flag staff (h) is the corresponding side to the height of the image formed on the screen ((3/4)h).
Next, we need to find the distance between the camera and the flag staff, which is given as 11m.
Using the concept of similar triangles, we can set up the following equation:
(3/4)h / 0.15m = h / 11m
Cross-multiplying, we get:
(3/4)h * 11m = h * 0.15m
Simplifying:
(33/4)h = 0.15h
Dividing both sides by h:
33/4 = 0.15
Now, we can solve for h by isolating it on one side:
h = (0.15 * 4) / 33
h ≈ 0.01818m
Therefore, the height of the flag staff is approximately 0.01818m or 18.18cm.