A person needs a lens of power –5.5 dioptres for correcting his distant vision. For correcting his near vision he needs a lens of power +1.5 dioptre. What is the focal length of the lens required for correcting (i) distant vision, and (ii) near vision?

Understanding Lens Power and Focal Length: The power of a lens, measured in dioptres, is inversely related to its focal length. The focal length, denoted as f, is calculated using the formula f = 1/P, where P is the power of the lens.

For correcting distant vision, a person requires a lens with a power of -5.5 dioptres. This negative value indicates a concave lens, typically used to correct myopia (near-sightedness).

To find the focal length for the distant vision lens, we apply the formula: f =1/−5.5. This calculation yields a focal length of approximately -0.182 meters, or -18.2 centimetres.

For near vision correction, the person needs a lens with a power of +1.5 dioptres. This positive value suggests a convex lens, commonly used for correcting hypermetropia (far-sightedness).

Applying the formula f = 1/1.5 for the near vision lens, we get a focal length of approximately 0.667 meters, or 66.7 centimetres.

These calculations demonstrate how lens power directly influences the focal length, which is crucial for designing glasses that correct specific vision impairments. The distinct focal lengths for distant and near vision correction highlight the tailored approach needed for different visual deficiencies.

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