At a reading distance of 10 inches, how much magnification does a +10D lens provide?

To determine the magnification provided by a +10D lens at a reading distance of 10 inches, it is important to utilize the lens formula for magnification in optical systems.

The formula for magnification (M) of a lens is given by:

[ M = \frac{D}{D - d} ]

where D is the power of the lens in diopters (in this case, +10D) and d is the image distance, which can be approximated by the reading distance when using a lens for that purpose. Here, when working in inches, you’ll need to convert the distance into centimeters for calculating purposes since diopters are in meters.

However, a more straightforward way to find the magnification in terms of objects viewed through the lens is to use the simplified approximation for lenses. For a converging lens (like a +10D lens), magnification can also be approximated as the ratio of the focal length of the lens to the distance at which the object is observed.

The focal length (f) of a +10D lens can be calculated as:

[ f = \frac{1}{D} = \frac{1}{10} \text{ meters} = 0.