A thin lens with a focal length of 6.00 cm is used as a simple magnifier. What angular magnification is obtainable with the lens if the object is at the focal point?

검증된 단계별 안내

Understand the concept of angular magnification: Angular magnification (M) for a simple magnifier is defined as the ratio of the angular size of the image to the angular size of the object when viewed with the naked eye at the near point. For a lens, when the object is placed at the focal point, the angular magnification is given by the formula:

M = 1 + \frac{D}{f}

, where

D

is the near point distance (typically 25 cm for a normal human eye) and

f

is the focal length of the lens.

Substitute the given values into the formula: The focal length of the lens is

f = 6.00

cm, and the near point distance is

D = 25

cm. Substitute these values into the formula:

M = 1 + \frac{25}{6}

Simplify the fraction: Calculate the value of the fraction

\frac{25}{6}

to determine the contribution of the lens's focal length to the magnification.

Add 1 to the result of the fraction: After simplifying the fraction, add 1 to account for the additional magnification provided by the lens when the object is at the focal point.

Interpret the result: The final value represents the angular magnification obtainable with the lens when the object is placed at the focal point. This value indicates how much larger the object appears when viewed through the magnifier compared to the naked eye.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Focal Length

The focal length of a lens is the distance from the lens to the focal point, where parallel rays of light converge. In this case, a focal length of 6.00 cm indicates that light rays entering the lens parallel to its axis will converge at a point 6.00 cm away from the lens. This property is crucial for understanding how lenses form images and magnify objects.

Angular Magnification

Angular magnification is a measure of how much larger an object appears when viewed through a lens compared to the naked eye. It is defined as the ratio of the angle subtended by the image at the eye to the angle subtended by the object at the same eye without the lens. For a simple magnifier, this concept helps quantify the lens's effectiveness in enlarging the apparent size of an object.

Simple Magnifier

A simple magnifier is a type of lens, typically a convex lens, used to produce a magnified image of an object. When the object is placed at or near the focal point of the lens, the lens creates a virtual image that appears larger than the object itself. Understanding how a simple magnifier works is essential for calculating the angular magnification and appreciating its practical applications in various fields.