A person can see up to 3m clearly, but can`t see up to 12 m. What is the power of lens required to see the object at 12 m.......?

To determine the power of the lens required for a person who can see clearly up to 3 meters but struggles to see objects at 12 meters, we need to understand a few concepts related to optics, particularly the lens formula and the concept of power.

Understanding the Basics

The ability to see clearly at different distances is often related to the eye's focal length and the need for corrective lenses. In this case, the person has a near point (the closest distance at which they can see clearly) of 3 meters and a far point (the furthest distance at which they can see clearly) of 12 meters. Since they can see clearly at 3 meters but not at 12 meters, they likely need a converging lens (a convex lens) to correct their vision for distant objects.

Lens Formula

The lens formula is given by:

1/f = 1/v - 1/u

Where:

• f = focal length of the lens (in meters)
• v = image distance (the distance from the lens to the image, which is positive for real images)
• u = object distance (the distance from the lens to the object, which is negative for real objects)

Applying the Lens Formula

In this scenario, we want the person to see an object at 12 meters clearly. Therefore:

• v = +12 m (the image distance, since the object is real and on the opposite side of the lens)
• u = -3 m (the object distance, since the person can see clearly only up to 3 m)

Now, substituting these values into the lens formula:

1/f = 1/v - 1/u

1/f = 1/12 - 1/(-3)

1/f = 1/12 + 1/3

To combine these fractions, we need a common denominator, which is 12:

1/f = 1/12 + 4/12 = 5/12

Now, taking the reciprocal gives us:

f = 12/5 = 2.4 m

Calculating the Power of the Lens

The power of a lens (P) is given by the formula:

P = 1/f (in meters)

Substituting the focal length we found:

P = 1/(2.4 m) = 0.4167 diopters

To express this in a more standard form, we can convert it to a more understandable value:

P ≈ +4.17 D

Summary

In conclusion, the power of the lens required for the person to see objects clearly at 12 meters is approximately +4.17 diopters. This positive value indicates that a convex lens is needed to correct their vision for distant objects.