How many diopters of power are required to focus parallel rays of light at a distance of 1 m?

To determine how many diopters of power are required to focus parallel rays of light at a distance of 1 meter, it is essential to understand the relationship between diopters and focal length. The power of a lens in diopters is defined as the reciprocal of the focal length in meters.

In this case, to focus parallel rays of light (which would be rays coming from an object at infinity) at a distance of 1 meter, the focal length of the lens must also be 1 meter. According to the formula for lens power, the power ( P ) in diopters is calculated as follows:

[ P = \frac{1}{f} ]

where ( f ) is the focal length in meters. Since the focal length is 1 meter:

[ P = \frac{1}{1} = 1 \text{ diopter} ]

Thus, the correct answer is one diopter. This means that a lens with a power of one diopter will effectively focus parallel rays of light to a point 1 meter from the lens, confirming the direct correlation between focal length and lens power.