A nearsighted person cannot clearly see beyond 200cm.find the power of the lens needed to see objects at large distances.

To determine the power of the lens needed for a nearsighted person who cannot see clearly beyond 200 cm, we first need to understand a few key concepts related to optics and vision correction. Nearsightedness, or myopia, occurs when the eye focuses images in front of the retina instead of directly on it. This means that objects at a distance appear blurry. To correct this, we can use a concave lens that diverges light rays, allowing the person to see distant objects clearly.

Understanding Lens Power

The power of a lens is measured in diopters (D), which is the reciprocal of the focal length (f) in meters. The formula to calculate the power (P) of a lens is:

P = 1/f

Where:

• P is the power of the lens in diopters.
• f is the focal length in meters.

Calculating the Focal Length

For a nearsighted person who can see clearly only up to 200 cm (or 2 meters), we need to find the focal length of the lens that will allow them to see objects at infinity (which is considered to be beyond 6 meters for practical purposes). The focal length of the lens required can be calculated using the following relationship:

f = -d

Here, d is the distance at which the person can see clearly, and it is negative because we are dealing with a diverging lens. In this case, d = 2 m, so:

f = -2 m

Calculating the Power of the Lens

Now that we have the focal length, we can substitute it into the power formula:

P = 1/f

P = 1/(-2)

P = -0.5 D

This means that the power of the lens needed to correct the nearsightedness is -0.5 diopters. The negative sign indicates that it is a concave lens, which is used to correct myopia.

Practical Implications

In practical terms, this means that the person would need glasses or contact lenses with a power of -0.5 D to see distant objects clearly. It’s important to note that the actual prescription may vary based on individual needs and should be determined by an eye care professional.

In summary, for a nearsighted individual who can only see clearly up to 200 cm, the required lens power to see distant objects clearly is -0.5 diopters. This correction allows light rays from distant objects to focus properly on the retina, enabling clear vision.