Two 28.0-cm-focal-length converging lenses are placed 16.5 cm apart. An object is placed 35.0 cm in front of one lens.
(a) Where will the final image formed by the second lens be located?
(b) What is the total magnification?

검증된 단계별 안내

Step 1: Start by analyzing the first lens. Use the lens formula \( \frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i} \), where \( f \) is the focal length, \( d_o \) is the object distance, and \( d_i \) is the image distance. For the first lens, \( f = 28.0 \, \text{cm} \) and \( d_o = 35.0 \, \text{cm} \). Solve for \( d_i \), the image distance for the first lens.

Step 2: Determine the position of the image formed by the first lens relative to the second lens. The lenses are 16.5 cm apart, so calculate the distance of the image from the second lens by subtracting the distance between the lenses from \( d_i \) of the first lens. This new distance becomes the object distance \( d_o \) for the second lens.

Step 3: Analyze the second lens using the lens formula \( \frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i} \). For the second lens, \( f = 28.0 \, \text{cm} \) and \( d_o \) is the distance calculated in Step 2. Solve for \( d_i \), the image distance for the second lens, which gives the location of the final image.

Step 4: Calculate the magnification for each lens using the formula \( M = -\frac{d_i}{d_o} \). For the first lens, use the values of \( d_i \) and \( d_o \) from Step 1. For the second lens, use the values of \( d_i \) and \( d_o \) from Step 3.

Step 5: Determine the total magnification by multiplying the magnifications of the two lenses: \( M_{\text{total}} = M_1 \times M_2 \). This gives the overall magnification of the system.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

10m

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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 based on the object's position and the lens's focal length.

Magnification

Magnification is the ratio of the height of the image to the height of the object, and it can also be calculated using the formula M = -v/u, where v is the image distance and u is the object distance. This concept helps in understanding how much larger or smaller the image appears compared to the object.

Converging Lenses

Converging lenses, or convex lenses, are thicker at the center than at the edges and focus parallel incoming light rays to a point known as the focal point. Understanding how these lenses work is crucial for analyzing the behavior of light as it passes through multiple lenses in a system.