Chapter 34: Problem 41
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. (a) Find the location and height of the image (call it \(I_1\)) formed by the lens with a focal length of 40.0 cm. (b) \(I_1\) is now the object for the second lens. Find the location and height of the image produced by the second lens. This is the final image produced by the combination of lenses.
Short Answer
Step by step solution
Understand the Lens Formula
Calculate Image Location for the First Lens
Calculate Image Height for the First Lens
Determine Object Distance for the Second Lens
Calculate Image Location for the Second Lens
Calculate Image Height for the Second Lens
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Lens Formula
- Focal Length (\( f \)): This is a constant that represents the distance over which initially parallel rays converge (or appear to converge) after passing through the lens.
- Object Distance (\( d_o \)): It’s the distance from the object to the lens. By convention, it is negative if the object is in front of the lens.
- Image Distance (\( d_i \)): This is the distance from the lens to the image. It is positive if the image is on the opposite side of the object relative to the lens.
Image Distance Calculation
Image Height Calculation
- With \( d_i = 22.22 \) cm and \( d_o = -50.0 \) cm, the magnification is: \( m = -\frac{22.22}{-50.0} = 0.444 \).
- The original object is 1.20 cm tall, therefore, using the equation: \( h_i = m \times h_o = 0.444 \times 1.20 \).
Lens Magnification
- If \( |m| > 1 \), the image is larger than the object.
- If \( |m| < 1 \), the image is smaller than the object.
- A positive magnification indicates an upright image, while a negative magnification indicates an inverted image.
Focal Length
- Designing optical systems, since focal lengths affect the magnification and image positions.
- Predicting how a lens will focus light or how multiple optical components will interact.