A farsighted person cannot see object placed closer to 50cm .Find the power of the lens needed to see the object at large distance

To determine the power of the lens needed for a farsighted person who struggles to see objects closer than 50 cm, we first need to understand a few key concepts related to optics and vision correction.

Understanding Farsightedness

Farsightedness, or hyperopia, occurs when the eye is unable to focus on nearby objects. This is often due to the eyeball being too short or the cornea having insufficient curvature. As a result, light entering the eye focuses behind the retina instead of directly on it. To correct this, a converging lens (convex lens) is used to help focus light correctly onto the retina.

Determining the Focal Length

The first step in finding the power of the lens is to calculate the focal length required for the lens. The formula for the lens formula is:

1/f = 1/v - 1/u

Where:

• f = focal length of the lens (in meters)
• v = image distance (distance from the lens to the retina, which we can assume to be around 25 cm or 0.25 m for a normal eye)
• u = object distance (the distance at which the person can see clearly, which is 50 cm or 0.5 m in this case)

Calculating the Focal Length

Plugging in the values into the lens formula:

1/f = 1/v - 1/u

Substituting the known values:

1/f = 1/0.25 - 1/0.5

Calculating each term:

• 1/0.25 = 4
• 1/0.5 = 2

Now, substituting these values back into the equation:

1/f = 4 - 2 = 2

This gives us:

f = 1/2 = 0.5 m

Finding the Power of the Lens

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

P = 1/f

Where P is in diopters (D) and f is in meters. Since we found f to be 0.5 m:

P = 1/0.5 = 2 D

Conclusion

Therefore, the power of the lens needed for the farsighted person to see objects clearly at a distance of 50 cm is +2 diopters. This positive value indicates that a converging lens is required to correct their vision.