To calculate the focal length (f) of a lens, we use the formula f = 1/P, where P is the power of the lens in dioptres.
For distant vision correction with a lens of power -5.5 dioptres, the focal length is f = 1/−5.5 which equals approximately -0.182 meters or -18.2 centimetres.
For near vision correction with a lens of power +1.5 dioptres, the focal length is f = 1/1.5 which equals approximately 0.667 meters or 66.7 centimetres.
Let’s discuss in detail
Calculating Focal Length for Vision Correction
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.
Correcting Distant Vision
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).
Focal Length for Distant Vision
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.
Correcting Near Vision
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).
Focal Length for Near Vision
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.