Ch. 33 - Lenses and Optical Instruments

Giancoli Douglas - Physics for Scientists and Engineers 5th edition

Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179당신이 사용하는 게 아니라요?교과서 변경

Giancoli Douglas 5th edition

Ch. 33 - Lenses and Optical Instruments

문제 5

32장, 문제 5

A 105-mm-focal-length lens is used to focus an image on the sensor of a camera. The maximum distance allowed between the lens and the sensor plane is 132 mm.
(a) How far in front of the sensor should the lens (assumed thin) be positioned if the object to be photographed is 10.0 m away? (b) 3.0 m away? (c) 1.0 m away?
(d) What is the closest object this lens could photograph sharply?

검증된 단계별 안내

Step 1: Understand the problem and identify the relevant formula. This is a thin lens problem, and we will use the lens equation:

\frac{1}{f} = \frac{1}{d}

_o + 1d_i, where

f

is the focal length,

d

_o is the object distance, and

d

_i is the image distance.

Step 2: Rearrange the lens equation to solve for the image distance

d

_i:

d

_i = f∗d_o / (d_o - f). This will allow us to calculate the position of the lens for each object distance.

Step 3: For part (a), substitute the given values into the formula:

f = 105

mm and

d

_o = 10.0 m (convert to mm:

d

_o = 10000 mm). Calculate

d

_i using the formula.

Step 4: Repeat the calculation for part (b) with

d

_o = 3.0 m (convert to mm:

d

_o = 3000 mm) and for part (c) with

d

_o = 1.0 m (convert to mm:

d

_o = 1000 mm).

Step 5: For part (d), determine the closest object distance by setting the image distance

d

_i to its maximum value of 132 mm (the maximum distance allowed between the lens and the sensor plane). Rearrange the lens equation to solve for

d

_o:

d

_o = f∗d_i / (d_i - f). Substitute

f = 105

mm and

d

_i = 132 mm to find the closest object distance.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

11m

주요 개념

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

Lens Formula

The lens formula relates the focal length (f) of a lens to the object distance (u) and the image distance (v) through the equation 1/f = 1/u + 1/v. This formula is essential for determining how far the lens should be positioned from the sensor to achieve a sharp image of an object at a given distance.

Thin Lens Approximation

The thin lens approximation assumes that the thickness of the lens is negligible compared to the distances involved. This simplification allows us to use the lens formula without accounting for lens thickness, making calculations more straightforward when dealing with ideal lenses.

Magnification

Magnification is the ratio of the height of the image to the height of the object, and it can also be expressed as the negative ratio of the image distance to the object distance (M = -v/u). Understanding magnification helps in assessing how the size of the image changes with respect to the object distance, which is relevant when positioning the lens for different object distances.