What is the focal length of the lens?

In summary, the focal length of a lens is the distance between the lens and the point where light rays converge to form a sharp image, typically measured in millimeters. It is determined by the curvature of the lens surfaces and the refractive index of the material, as well as the distance between the lens and the object being viewed. A shorter focal length results in a wider field of view and lower magnification, while a longer focal length results in a narrower field of view and higher magnification. The focal length can also affect image quality, such as distortion, sharpness, depth of field, and amount of light. While the focal length of a lens is fixed, the field of view and magnification can be adjusted by using different lenses
  • #1
keemosabi
109
0

Homework Statement


When a diverging lens is held 12 cm above a line of print, as in Figure 26.29, the image is 4.1 cm beneath the lens. What is the focal length of the lens?
26-29fig.gif



Homework Equations


1/di + 1/do = 1/f


The Attempt at a Solution


1/di + 1/do = 1/f
1/4.1 + 1/12 = 1/f
f = 3.0559 cm

What did I do wrong?
 
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  • #2
The image is virtual, so di is considered to be negative.
 
  • #3


Your solution is correct. The focal length of the lens is 3.0559 cm. It is possible that the numbers were rounded differently in the original problem, which could account for a slightly different answer. Additionally, make sure to pay attention to the units when solving the equation - in this case, both distances should be in centimeters.
 

1. What is the focal length of a lens?

The focal length of a lens is the distance between the lens and the point where light rays converge to form a sharp image. It is typically measured in millimeters (mm) and is an important factor in determining the magnification and field of view of the lens.

2. How is the focal length of a lens determined?

The focal length of a lens is determined by the curvature of its surfaces and the refractive index of the material it is made of. It is also affected by the distance between the lens and the object being viewed or photographed.

3. What is the difference between a short and a long focal length lens?

A short focal length lens has a shorter distance between the lens and the point of convergence, resulting in a wider field of view and a lower magnification. On the other hand, a long focal length lens has a longer distance between the lens and the point of convergence, resulting in a narrower field of view and a higher magnification.

4. How does the focal length affect the image quality?

The focal length of a lens can affect the image quality in several ways. A shorter focal length can cause distortion in the image, while a longer focal length can reduce distortion but may also result in a loss of sharpness. Additionally, the focal length can also affect the depth of field and the amount of light that enters the lens.

5. Can the focal length of a lens be changed?

The focal length of a lens is a fixed characteristic and cannot be changed. However, the field of view and magnification can be adjusted by using different lenses or by using zoom lenses, which have variable focal lengths. Some cameras also have interchangeable lenses that can be used to change the focal length for different purposes.

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