Finding distance of image from mirror given focal length

In summary, the problem involves finding the distance from an object at a large distance to a concave mirror with a focal length of 40cm. The equation 1/u + 1/v = 1/f is used to solve for the distance, and the image is determined to be real due to its placement outside the focus. However, the given information may not be enough to solve the problem, and a key provides the answer of 40cm. When a large number is substituted for the object distance, the image distance also increases.
  • #1
RabbitWho
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Homework Statement


An object is at a very large distance from a concave mirror of focal length 40cm. Find the distance from the image to the mirror. Is the image real or virtual?

Homework Equations


1/u + 1/v = 1/f

The Attempt at a Solution


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1/u + 1/v = 1/40

The image has to be real because it must be outside the focus if it is very far from the mirror, right?
It seems to me like I haven't got enough information to solve the problem. How would I go about doing it? The answer from the key is 40cm.
 
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  • #2
What do you get if you put in a very large number (say, 10000cm) for the object distance? What happens as that distance gets even farther?
 
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Likes RabbitWho

1. How do I calculate the distance of an image from a mirror given the focal length?

To calculate the distance of an image from a mirror, you can use the formula: d = f * (1 + 1/m), where d is the distance of the image from the mirror, f is the focal length of the mirror, and m is the magnification of the mirror.

2. What is the focal length of a mirror?

The focal length of a mirror is the distance between the mirror and the point where all the light rays parallel to the principal axis converge after reflecting off the mirror. It is usually denoted by the letter "f".

3. How do I determine the magnification of a mirror?

The magnification of a mirror is given by the formula: m = -i/o, where m is the magnification, i is the distance of the image from the mirror, and o is the distance of the object from the mirror. A negative magnification indicates an inverted image, while a positive magnification indicates an upright image.

4. Can the distance of an image from a mirror be negative?

Yes, the distance of an image from a mirror can be negative. This indicates that the image is located behind the mirror, which is common in concave mirrors. A positive distance indicates that the image is located in front of the mirror.

5. Why is it important to know the distance of an image from a mirror?

The distance of an image from a mirror is important because it allows us to determine the size and position of the image formed by the mirror. This information is crucial for understanding the properties and behavior of mirrors, which are essential in many scientific and technological applications.

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