A farsighted person cannot clearly see beyond 200 cm. Find the power of the lens needed to see the objects at 20 cm.

To determine the power of the lens required for a farsighted person who cannot see clearly beyond 200 cm and needs to see objects at 20 cm, we can use the lens formula and the concept of lens power. Let's break this down step by step.

Understanding Farsightedness

Farsightedness, or hyperopia, occurs when the eye is unable to focus on nearby objects clearly. This happens because the light entering the eye focuses behind the retina. In this case, the person can see objects clearly at a distance but struggles with closer ones.

Using the 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 (in meters)
• u = object distance (in meters)

Identifying the Values

In this scenario:

• The object distance (u) is -20 cm (we use a negative sign because the object is on the same side as the incoming light).
• The image distance (v) is +200 cm (the distance at which the person can see clearly).

Now, we need to convert these distances into meters:

• u = -0.20 m
• v = 2.00 m

Calculating the Focal Length

Plugging these values into the lens formula:

1/f = 1/v - 1/u

1/f = 1/2.00 - 1/(-0.20)

1/f = 0.5 + 5

1/f = 5.5

Now, taking the reciprocal to find the focal length:

f = 1/5.5 ≈ 0.1818 m

Finding 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 = 1/0.1818 ≈ 5.5 D

Final Result

The power of the lens needed for the farsighted person to see objects clearly at 20 cm is approximately +5.5 diopters. This positive value indicates that a converging lens is required to help focus the light correctly onto the retina for nearby objects.