A small object is 25.0 cm from a diverging lens as shown in...

Name: Problem 90, Chapter 23: Physics: Principles with Applications
Uploaded: 2019-05-10T00:22:31-08:00
Duration: 2 min 22 s
Channel: Kyle Godbey
Description: A small object is 25.0 cm from a diverging lens as shown in Fig. 23-68. A converging lens with a focal length of 12.0 cm is 30.0 cm to the right of the diverging lens. The two-lens system forms a real inverted image 17.0 cm to the right of the converging lens. What is the focal length of the diverging lens? FIGURE 23–68 Problem 90. (FIGURE CAN'T COPY)

A small object is 25.0 cm from a diverging lens as shown in Fig. 23-68. A converging lens with a focal length of 12.0 cm is 30.0 cm to the right of the diverging lens. The two-lens system forms a real inverted image 17.0 cm to the right of the converging lens. What is the focal length of the diverging lens? FIGURE 23–68 Problem 90. (FIGURE CAN'T COPY)

Key Concepts

Diverging Lenses

Diverging lenses, also known as concave lenses, have the property of spreading out light rays that are initially parallel. They always produce virtual, upright, and reduced images when used with a single object. Their focal lengths are conventionally taken as negative, which affects the application of the thin lens formula.

Thin Lens Equation

This is a fundamental relation in geometric optics that connects the object distance, image distance, and focal length of a lens. It is usually written as 1/f = 1/d_o + 1/d_i, where f is the focal length, d_o is the object distance, and d_i is the image distance. This equation is essential for solving problems involving image formation by lenses.

Optical Sign Conventions

In lens problems, sign conventions determine whether distances are considered positive or negative. For example, object distances are typically positive if the object is on the same side of the lens as the incoming light, while focal lengths can be positive for converging lenses and negative for diverging lenses. Mastery of these conventions is crucial in correctly applying the thin lens equation.

Converging Lenses

Converging lenses, or convex lenses, have the ability to bring parallel rays of light to a focus, forming real images if the object is placed outside the focal length. They usually have positive focal lengths, and they are used in many optical instruments to create enlarged, real images.

Multiple Lens Systems

When dealing with systems that include more than one lens, each lens is treated individually using the lens equation. The image formed by the first lens acts as an object for the second lens. This sequential approach is key to analyzing the overall behavior of multi-lens systems and solving for unknown parameters.

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