What is the power of a lens with a focal length of 25 mm?

Verified step by step guidance

Understand the relationship between the power of a lens and its focal length. The formula to calculate the power \( P \) of a lens is \( P = \frac{1000}{f} \), where \( f \) is the focal length in millimeters, and \( P \) is measured in diopters (D).

Convert the given focal length into millimeters if it is not already in that unit. In this case, the focal length is already provided as \( f = 25 \ \text{mm} \).

Substitute the given focal length \( f = 25 \ \text{mm} \) into the formula \( P = \frac{1000}{f} \). This gives \( P = \frac{1000}{25} \).

Simplify the expression \( \frac{1000}{25} \) to find the power of the lens in diopters.

The result will give the power of the lens in diopters (D), which is a measure of the lens's ability to converge or diverge light.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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 that determines the lens's optical power and its ability to focus light. A shorter focal length indicates a stronger lens that can bend light more sharply, while a longer focal length indicates a weaker lens.

Lens Power

The power of a lens is defined as the reciprocal of its focal length, measured in meters. It is expressed in diopters (D), where a lens with a focal length of 1 meter has a power of 1 D. The formula for calculating lens power is P = 1/f, where P is the power in diopters and f is the focal length in meters. Thus, a lens with a shorter focal length has a higher power.

Diopters

Diopters are the unit of measurement for the optical power of a lens. One diopter corresponds to a lens with a focal length of one meter. This unit helps quantify how strongly a lens converges or diverges light, making it easier to compare different lenses. A lens with a power of +4 D, for example, has a focal length of 0.25 meters (25 mm), indicating it is a converging lens.

Related Practice

Textbook Question

What is the focal length of a second lens that could be placed in contact with the first lens to provide an overall power of 30 D?

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A camera takes a properly exposed photo at F5.6 and 1/125 s. What shutter speed should be used if the lens is changed to F4.0?

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