Calculate the dioptric value of a CR-39 lens with a radius of curvature of 0.645m.

To find the dioptric value of a lens, the formula used is:

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

where ( D ) is the power of the lens in diopters and ( f ) is the focal length in meters. The focal length can be calculated from the radius of curvature (R) using the lens maker's formula for a thin lens, which for a lens made from a material with a refractive index ( n ) is given as:

[ f = \frac{R}{n - 1} ]

For CR-39 lenses, a commonly used refractive index is approximately 1.5. So, substituting ( n ) and the radius of curvature into the formula, we proceed as follows:

Using ( R = 0.645 ) m and ( n = 1.5 ):

[ f = \frac{0.645 , m}{1.5 - 1} = \frac{0.645 , m}{0.5} = 1.29 , m ]

Now, we can calculate the power ( D ):

[ D = \frac{1}{f} = \frac{1}{1