A farsighted person has a near point (closest point they can see clearly) of 200 cm. What power and type of lens will correct this condition and allow the person to read a book at 25 cm?
To correct the farsightedness of a person, we need to determine the power and type of lens required. Farsightedness, also known as hyperopia, occurs when the eyeball is too short or the focusing power of the eye is too weak. This causes nearby objects to appear blurry while distant objects remain clear.
To find the lens power required, we can use the formula for lens power:
Lens Power = 1 / Focal Length
In this case, the near point of a farsighted person is given as 200 cm. The near point is the closest distance at which the person can see clearly without any correction. To determine the focal length, we can use the formula:
Focal Length = 1 / Near Point
Focal Length = 1 / 200 cm = 0.005 cm⁻¹
Now, to find the power of the corrective lens, we invert the focal length:
Lens Power = 1 / Focal Length
Lens Power = 1 / 0.005 cm⁻¹ = 200 diopters (D)
Therefore, a lens with a power of +200 D is required to correct the farsightedness of the person.
Regarding the lens type, a convex lens (also known as a converging lens) is used to correct farsightedness. A convex lens is thicker in the middle and thinner at the edges, causing light rays to converge before entering the eye and providing the necessary additional focusing power.
Hence, to correct the person's farsightedness and allow them to read a book at 25 cm, they would require a convex lens with a power of +200 D.