An image on the screen of a 12 cm long pinhole camera is 7cm. How large is the original object, if it is located 36 cm in front of the pinhole?
To find the size of the original object, we can use the concept of similar triangles. The ratio of the image size to the object size will be the same as the ratio of the distance from the image to the pinhole (the screen distance) to the distance from the object to the pinhole.
Let's call the size of the original object "O" and the distance from the pinhole to the object "d". We can set up the proportion:
(image size) / (object size) = (screen distance) / (object distance)
Plugging in the given values:
7 cm / O = 12 cm / d
To find the size of the original object, we need to solve for O. We can cross multiply and simplify the equation:
7 cm * d = 12 cm * O
Now, rearrange the equation to solve for O:
O = (7 cm * d) / 12 cm
Substituting d = 36 cm:
O = (7 cm * 36 cm) / 12 cm
O = 252 cm / 12 cm
O ≈ 21 cm
Therefore, the original object is approximately 21 cm long.
To determine the size of the original object, we can use similar triangles and the relationship between the object distance, image distance, and their respective sizes.
In this scenario, we have a pinhole camera setup where the image distance and size of the image on the screen are known, while the object distance is provided. We can use the formula for similar triangles:
(object size) / (object distance) = (image size) / (image distance)
Plugging in the known values:
(object size) / 36 cm = 7 cm / 12 cm
Now, we can cross-multiply and solve for the object size:
(object size) = (36 cm * 7 cm) / 12 cm
Calculating this:
(object size) = 252 cm²
Therefore, the original object has an area of 252 cm².