A near sighted person cannot clearly see beyond 200cm.Find the power of lens needed to see object at large distances.

To determine the power of the lens needed for a nearsighted person who can only see clearly up to 200 cm, we first need to understand a few key concepts about vision and lenses. Nearsightedness, or myopia, means that distant objects appear blurry because the eye focuses images in front of the retina. To correct this, we use a diverging lens, which helps to focus the light correctly onto the retina.

Understanding Lens Power

The power of a lens is measured in diopters (D) and is defined as the reciprocal of the focal length (f) in meters:

Power (P) = 1 / f

For a nearsighted person, the focal length of the lens must be such that it allows them to see objects at a distance clearly. Since this person can see clearly only up to 200 cm (or 2 meters), we need to find the focal length that will enable them to see objects at infinity (which is conventionally considered to be beyond 6 meters).

Calculating the Focal Length

To find the necessary focal length, we can use the following relationship:

Focal Length (f) = Distance of clear vision (d) - Distance of object (D)

In this case, the distance of clear vision (d) is 2 meters (200 cm), and we want to correct vision for objects at infinity (D = ∞). Therefore, we can simplify our calculation:

f = -2 m

The negative sign indicates that we are using a diverging lens, which is typical for correcting nearsightedness.

Finding the Power of the Lens

Now that we have the focal length, we can calculate the power of the lens:

P = 1 / f

Substituting the focal length:

P = 1 / (-2)

P = -0.5 D

Interpreting the Result

The negative value of the power indicates that this is a diverging lens, which is exactly what is needed for a nearsighted person. A lens with a power of -0.5 diopters will allow the individual to see distant objects clearly.

Practical Application

In practical terms, if this person were to wear glasses with a lens power of -0.5 D, they would be able to see objects at large distances without the blurriness caused by their nearsightedness. This correction is essential for activities such as driving, watching movies, or enjoying scenic views.

In summary, the power of the lens needed for a nearsighted person who can only see clearly up to 200 cm is -0.5 diopters. This calculation illustrates the relationship between focal length and lens power, providing a clear understanding of how corrective lenses function to improve vision.