Final answer:
The power of the eye when viewing an object 50.0 cm away is found using the thin lens equation and is approximately -52.0D for a normal eye. The power varies with the ability to focus, with a greater power needed for objects closer to the eye.
Step-by-step explanation:
Calculating the Power of the Eye
The power of the eye when viewing an object is determined based on the lens-to-retina distance and the distance from the object to the eye. To find the optical power in diopters (D), which is the inverse of the focal length in meters, the formula P = 1/f is used, where P is the power in diopters and f is the focal length in meters. When an object is 50.0 cm away, the eye must adjust its lens to form a clear image on the retina, given the lens-to-retina distance is typically around 2.00 cm for a normal eye.
For an object located 50.0 cm away, to calculate the eye's power, one would also need to take into account the relaxed state of the eye and its ability to accommodate different focal lengths.
In scenarios where the lens-to-retina distance is known, and the object distance is given, the formula can be applied by first finding the focal length using the thin lens equation 1/f = 1/do + 1/di, where do is the object distance and di is the image distance (lens-to-retina distance). For a normal eye viewing an object at 50.0 cm, assuming the lens-to-retina distance to be 2.00 cm, the calculation would show that the power of the eye is approximately -52.0D.
The power of an eye can vary greatly, depending on a person's ability to adjust focus, known as accommodation. For example, a woman who can see clearly at a distance as close as 8.00 cm has eyes with a significantly higher power due to the shorter focal distance required.
Understanding the power of the human eye is essential for diagnosing vision issues and prescribing corrective lenses. For instance, a farsighted person whose near point is 1.00 m may need a specific power of spectacle lenses to see objects closer to them clearly, such as at a distance of 25.0 cm.