How far away from the pinhole should you move the screen to obtain a 5cm high image of a girl who is 125cm tall and stands 250cm away from the camera?
To determine how far away from the pinhole you should move the screen to obtain a 5cm high image of a girl who is 125cm tall and stands 250cm away from the camera, we can use the principles of similar triangles and the lens formula.
Step 1: Understand the problem.
We are given the height of the girl (125cm), her distance from the camera (250cm), and we need to find the distance from the pinhole to the screen.
Step 2: Identify the similar triangles.
In this case, we can consider two triangles: the triangle formed by the girl, the camera, and the screen, and the triangle formed by the girl, the pinhole, and the screen.
Step 3: Set up the proportions.
The height of the image (5cm) is related to the height of the girl (125cm) and their respective distances from the camera and the pinhole. We can set up the proportion as follows:
(Height of the image) / (Distance from the camera to the object) = (Height of the object) / (Distance from the pinhole to the object)
Substituting the values we have:
5cm / 250cm = 125cm / (Distance from the pinhole to the object)
Step 4: Solve for the unknown.
Cross-multiplying the proportion, we get:
5cm * (Distance from the pinhole to the object) = 125cm * 250cm
Dividing both sides by 5cm gives us:
Distance from the pinhole to the object = (125cm * 250cm) / 5cm
Calculating this expression gives us the distance from the pinhole to the object, which will be the distance from the pinhole to the screen needed for the 5cm high image.