Ch 34: Geometric Optics

Young & Freedman Calc - University Physics 14th Edition

Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610당신이 사용하는 게 아니라요?교과서 변경

Young & Freedman Calc 14th Edition

Ch 34: Geometric Optics

문제 36

34장, 문제 36

A lensmaker wants to make a magnifying glass from glass that has an index of refraction n = 1.55 and a focal length of 20.0 cm. If the two surfaces of the lens are to have equal radii, what should that radius be?

검증된 단계별 안내

Start with the lensmaker's equation:

\frac{1}{f} = (n - 1) * (\frac{1}{R} - \frac{1}{R'})

, where

f

is the focal length,

n

is the index of refraction, and

R

and

R'

are the radii of curvature of the two surfaces.

Since the two surfaces of the lens are to have equal radii, set

R = - R'

(the negative sign accounts for the opposite curvature directions). Substitute this into the lensmaker's equation:

\frac{1}{f} = (n - 1) * (\frac{1}{R} - \frac{1}{-}).

Simplify the equation:

\frac{1}{f} = (n - 1) * (\frac{1}{R} + \frac{1}{R}) = (n - 1) * \frac{2}{R} .

Rearrange the equation to solve for

R

R = \frac{2}{f * (n - 1)} .

Substitute the given values:

f = 20.0

cm and

n = 1.55

. This will allow you to calculate the radius

R

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

도움이 되었나요?

주요 개념

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

Lensmaker's Equation

The Lensmaker'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. For a lens with equal radii, R1 = R2 = R, simplifying the equation significantly.

Index of Refraction

The index of refraction (n) is a dimensionless number that describes how light propagates through a medium. It is defined as the ratio of the speed of light in a vacuum to the speed of light in the medium. A higher index indicates that light travels slower in that medium, affecting how light bends when entering or exiting the lens, which is crucial for determining the lens's focal length.

Focal Length

The focal length of a lens is the distance from the lens to the focal point, where parallel rays of light converge after passing through the lens. It is a key parameter in lens design, influencing the magnification and image formation. In this scenario, the focal length is given as 20.0 cm, which is essential for calculating the required radius of curvature for the lens surfaces.