Question

An object 3.00 m high is placed at a distance of 7.50 m from a pinhole camera. If the image height is 6.00 cm, what is the distance of the film from the pinhole?

a) 0.15 m
b) 0.20 m
c) 0.25 m
d) 0.30 m

Answer 1

To find the distance of the film from the pinhole, one uses ratios from similar triangles. The correct distance for the given problem is 0.15 m, calculated using the object and image sizes and distances.

Step-by-step explanation:

The question pertains to the calculation of the distance between the film and the pinhole in a pinhole camera to produce a certain image size given the object size and distance. To find this distance, we can use proportional reasoning based on similar triangles formed by the object and its image inside the camera. The respective heights and distances for the object and image form proportional ratios.

The ratio can be represented as:
Object height / Image height = Object distance / Image distance
Plugging the values we get:
3.00 m / 0.06 m = 7.50 m / Image distance
Solving this, Image distance = (0.06 m * 7.50 m) / 3.00 m
Therefore, Image distance = 0.15 m

This calculation is a common problem in geometric optics and relates to the principles of similar triangles and lens imaging.