Without glasses, your uncle Albert can see things clearly only if they are between 25.1 cm and 190 cm from his eyes. What power eyeglass lens will correct your uncle's myopia? Assume the lenses will sit 1.70 cm from his eyes. Give answer in diopters. Do not enter unit.
What is your uncle's near point when wearing these glasses?
To find the power of the eyeglass lens that will correct your uncle's myopia, we can use the formula:
Lens Power = 1 / focal length
First, let's convert the near point range from centimeters to meters for consistency. The near point range is 25.1 cm to 190 cm, which is equivalent to 0.251 m to 1.9 m.
Since the lenses will sit 1.70 cm from his eyes, the focal length can be calculated by subtracting the distance the lenses sit from the near point range:
Focal length = Near point distance - Distance from the lenses to the eyes
For the lower range of 0.251 m:
Focal length = 0.251 m - 0.017 m = 0.234 m
For the upper range of 1.9 m:
Focal length = 1.9 m - 0.017 m = 1.883 m
Next, we calculate the lens powers for both the lower and upper ranges using the lens power formula:
Lens Power = 1 / focal length
For the lower range:
Lens Power = 1 / 0.234 m ≈ 4.27 diopters
For the upper range:
Lens Power = 1 / 1.883 m ≈ 0.53 diopters
To find your uncle's near point when wearing these glasses, we need to calculate the distance at which he can see things clearly. The near point is the closest distance from the eye that an individual can focus on an object clearly. In this case, with the glasses correcting his myopia, the near point would be the lower range of 25.1 cm.
Therefore, your uncle's near point when wearing these glasses is 25.1 cm.