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Ch 35: Optical Instruments
Knight Calc - Physics for Scientists and Engineers 5th Edition
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796당신이 사용하는 게 아니라요?교과서 변경
35장, 문제 34

The cornea, a boundary between the air and the aqueous humor, has a 3.0 cm focal length when acting alone. What is its radius of curvature?

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1
Step 1: Understand the relationship between the focal length and the radius of curvature for a lens or curved surface. The formula to use is the Lensmaker's equation for a single refractive surface: \( R = 2f \), where \( R \) is the radius of curvature and \( f \) is the focal length.
Step 2: Identify the given values in the problem. The focal length \( f \) is provided as 3.0 cm.
Step 3: Substitute the given focal length into the formula \( R = 2f \). This means \( R = 2 \times 3.0 \, \text{cm} \).
Step 4: Perform the multiplication to find the radius of curvature. This step involves calculating \( R \) using the formula.
Step 5: Interpret the result. The radius of curvature \( R \) represents the distance from the center of the cornea's curvature to its surface, and it is directly proportional to the focal length.

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주요 개념

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Focal Length

The focal length of a lens or mirror is the distance from the lens or mirror to the focal point, where parallel rays of light converge. In optics, the focal length is crucial for determining how a lens will bend light and is inversely related to the curvature of the lens. A shorter focal length indicates a more powerful lens that can bend light more sharply.
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가이드 코스
10:54
Spinning on a string of variable length

Radius of Curvature

The radius of curvature is the radius of the sphere from which a lens or mirror segment is taken. It is a measure of how 'curved' the surface is; a smaller radius indicates a steeper curve. In the context of lenses, the radius of curvature is directly related to the focal length, as described by the lens maker's equation.
추천 영상:
가이드 코스
06:18
Calculating Radius of Nitrogen

Lens Maker's Equation

The lens maker's equation relates the focal length of a lens to the radii of curvature of its two surfaces and the refractive index of the material. It is expressed as 1/f = (n - 1) * (1/R1 - 1/R2), where f is the focal length, n is the refractive index, and R1 and R2 are the radii of curvature of the lens surfaces. This equation is essential for calculating the radius of curvature when the focal length and refractive index are known.
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가이드 코스
05:38
Lens Maker Equation
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