The power of a lens (P) is related to its focal length (f) by the formula P = 1/f, where f is in meters. For a lens with a power of +1.5 D, the focal length is f = 1/1.5 meters, which equals approximately 0.67 meters or 67 cm. The positive sign of the power indicates that the lens is a converging lens, typically used to correct farsightedness.
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Introduction to Lens Power and Focal Length
Understanding Lens Power: The power of a lens, measured in dioptres (D), is a key optical property that indicates its ability to converge or diverge light. It is directly related to the focal length of the lens, providing insight into its function.
Lens Power Prescribed by Doctor: A doctor has prescribed a corrective lens with a power of +1.5 dioptres. The positive value of the power suggests a specific type of lens, which can be identified by calculating its focal length.
Calculating Focal Length
Using the Power Formula: The relationship between the power (P) of a lens and its focal length (f) is given by P = 1/f, where f is expressed in meters. To find the focal length of a lens with a power of +1.5 D, we rearrange this formula to f = 1/P.
Determining the Focal Length
Focal Length Calculation: Substituting the power value into the formula, f = 1/1.5, we find that the focal length is approximately 0.67 meters or 67 cm. This value is crucial in identifying the type of lens.
Identifying the Type of Lens
Nature of the Lens: The positive focal length indicates that the lens is a converging lens. Converging lenses, such as convex lenses, are characterized by their ability to bring light rays together.
Characteristics of the Prescribed Lens: Therefore, a lens with a power of +1.5 dioptres has a focal length of approximately 67 cm and is a converging lens. This type of lens is commonly used in corrective eyewear to address issues like farsightedness, where converging lenses help focus light onto the retina.