A 1.20 cm tall object is 50.0 cm to the left of a converging lens of focal length 40.0 cm. A second converging lens, this one having a focal length of 60.0 cm, is located 300.0 cm to the right of the first lens along the same optic axis. Find the location and height of the image (call it I1) formed by the lens with a focal length of 40.0 cm.

검증된 단계별 안내

Step 1: Use the lens formula to find the image distance (\(d_i\)) for the first lens. The lens formula is \(\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}\), where \(f\) is the focal length of the lens, \(d_o\) is the object distance, and \(d_i\) is the image distance. Substitute \(f = 40.0\ \text{cm}\) and \(d_o = 50.0\ \text{cm}\) into the formula.

Step 2: Rearrange the lens formula to solve for \(d_i\): \(\frac{1}{d_i} = \frac{1}{f} - \frac{1}{d_o}\). Perform the subtraction of the reciprocals of \(f\) and \(d_o\) to find \(\frac{1}{d_i}\), then take the reciprocal to find \(d_i\).

Step 3: Determine the magnification (\(M\)) of the first lens using the formula \(M = -\frac{d_i}{d_o}\). Substitute the values of \(d_i\) and \(d_o\) to calculate \(M\).

Step 4: Calculate the height of the image (\(h_i\)) formed by the first lens using the magnification formula \(h_i = M \cdot h_o\), where \(h_o = 1.20\ \text{cm}\) is the height of the object. Substitute the values of \(M\) and \(h_o\) to find \(h_i\).

Step 5: Summarize the results for the first image (\(I_1\)): its location (\(d_i\)) relative to the first lens and its height (\(h_i\)). These values will be used as inputs for further calculations involving the second lens in subsequent parts of the problem.

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.

Lens Formula

The lens formula relates the object distance (u), image distance (v), and focal length (f) of a lens, expressed as 1/f = 1/v - 1/u. This formula is essential for determining the position of the image formed by a lens. In this scenario, it will help calculate the image location (I1) created by the first converging lens.

Magnification

Magnification (M) is the ratio of the height of the image (h') to the height of the object (h), given by M = h'/h = -v/u. This concept is crucial for understanding how the size of the image relates to the size of the object. In this problem, it will be used to find the height of the image formed by the first lens.

Converging Lens

A converging lens, or convex lens, is thicker at the center than at the edges and causes parallel rays of light to converge at a focal point. The focal length is the distance from the lens to this point. Understanding the behavior of converging lenses is vital for analyzing how they form images, especially in multi-lens systems like the one described in the question.