BIO Ordinary Glasses. Ordinary glasses are worn in front of the eye and usually 2.0 cm in front of the eyeball. Suppose that the person in Exercise 34.52 prefers ordinary glasses to contact lenses. What focal length lenses are needed to correct his vision, and what is their power in diopters?

검증된 단계별 안내

Understand the problem: The goal is to determine the focal length of the glasses and their power in diopters. The glasses are positioned 2.0 cm in front of the eye, and the correction is for the person's vision. The focal length is related to the lens's ability to focus light, and the power in diopters is given by the formula \( P = \frac{1}{f} \), where \( f \) is the focal length in meters.

Identify the key parameters: From the problem, the glasses are 2.0 cm (or 0.02 m) in front of the eye. Use the information from Exercise 34.52 (not provided here) to determine the near point or far point of the person's vision, as this will help calculate the required focal length.

Apply the lens formula: The lens formula is \( \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \), where \( f \) is the focal length, \( v \) is the image distance (distance from the lens to the corrected near or far point), and \( u \) is the object distance (distance from the lens to the uncorrected near or far point). Adjust \( v \) to account for the 2.0 cm distance of the glasses from the eye.

Solve for the focal length \( f \): Rearrange the lens formula to isolate \( f \). Substitute the values for \( v \) and \( u \) based on the person's vision correction needs. Ensure all distances are in meters for consistency.

Calculate the power in diopters: Once the focal length \( f \) is determined, calculate the power \( P \) using the formula \( P = \frac{1}{f} \). Express the result in diopters (D), which is the standard unit for lens power.

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주요 개념

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Focal Length

The focal length of a lens is the distance from the lens to the point where parallel rays of light converge or appear to diverge. It is a critical parameter in lens design, determining how strongly the lens converges or diverges light. For corrective lenses, the focal length must be adjusted to compensate for the individual's vision deficiencies, allowing them to see clearly.

Lens Power

Lens power, measured in diopters, is the reciprocal of the focal length in meters. A positive power indicates a converging lens (convex), while a negative power indicates a diverging lens (concave). The power of corrective lenses is essential for determining how much correction is needed for a person's vision, with higher absolute values indicating stronger lenses.

Optical Correction

Optical correction involves using lenses to adjust the focal point of light entering the eye, ensuring that images are focused on the retina. This is crucial for individuals with refractive errors, such as myopia or hyperopia. The distance of the glasses from the eye and the individual's specific vision needs must be considered when calculating the required focal length and power of the lenses.