How far from a piece of paper must you hold your father’s 2.00 D reading glasses to try to burn a hole in the paper with sunlight?
focal length is the reciprocal of 2.00, or 50 cm.
To determine the distance from a piece of paper that you need to hold your father's 2.00 D reading glasses in order to burn a hole in the paper with sunlight, you would need to consider the concept of focal length.
The focal length of a lens is the distance between the lens and the point where the light rays converge or diverge. For a convex lens like reading glasses, the focal length is given by the formula:
1/f = 1/do + 1/di
Where:
- f is the focal length of the lens,
- do is the object distance (distance between the lens and the object), and
- di is the image distance (distance between the lens and the focused image).
In this case, the object is the paper, and the image distance is the distance where the light rays converge to form a focal point intense enough to burn the paper.
Assuming the sunlight is effectively parallel, we can consider the object distance (do) to be very large, since the rays of light hitting the lens can be considered parallel.
Rearranging the formula, we get:
di = 1 / (1/f - 1/do)
Given that the focal length (f) of the reading glasses is 2.00 D, and assuming an object distance (do) of infinity (effectively parallel rays), we can calculate the image distance (di).
di = 1 / (1/2.00 - 1/infinity)
di = 1 / (0.5 - 0)
di = 1 / 0.5
di = 2.00 meters
Therefore, you would need to hold the reading glasses at a distance of approximately 2.00 meters from the piece of paper to try to burn a hole in the paper with sunlight.
Please note that this is a theoretical calculation and it's essential to exercise caution when working with intense light sources, as they can cause eye damage or fire hazards.