# Solve Mirror Equation for Unknown Image Distance & Focal Length

• zoop-loop
In summary, the problem involves an ant standing in front of a mirror and seeing its image, with the ant's height and the image's height given. The equations used are the mirror equation and the magnification equation, with p representing the object distance, q representing the image distance, f representing the focal length, h' representing the image height, and h representing the object height. The problem can be solved by setting up the mirror equation and using the magnification equation to link p and q. However, the solution beyond this point is unknown.
zoop-loop

## Homework Statement

An ant is 1.03 cm tall and stands 4.90 cm in front of an unknown mirror. To its surprise the ant sees an its image which is 4.43 cm tall! What is the the distance to the image? What is the focal length of the mirror?

## Homework Equations

The mirror equation: 1/p + 1/q = 1/f

p: object distance
q: image distance
f: focal length

Maybe the magnification equation?: M = -q/p = h'/h

q: image distance
p: object distance
h': image height
h: object height

## The Attempt at a Solution

I set the problem up this way:

1/4.90 + 1/q = 1/f

I have no idea how to figure it out beyond this point.

Please help!

Try to use the magnification equation... it links p and q.

## 1. What is the mirror equation?

The mirror equation is a mathematical formula that relates the distance of an object from a curved mirror to the distance of the image from the mirror, as well as the focal length of the mirror. It is represented as 1/do + 1/di = 1/f, where do is the distance of the object from the mirror, di is the distance of the image from the mirror, and f is the focal length of the mirror.

## 2. How do I solve the mirror equation for unknown image distance?

To solve the mirror equation for unknown image distance (di), simply rearrange the equation to di = 1/(1/do - 1/f). Plug in the known values for do and f, and solve for di. Remember to use the correct units for do and f (usually in meters) to get the image distance in the same units.

## 3. How do I solve the mirror equation for unknown focal length?

To solve the mirror equation for unknown focal length (f), rearrange the equation to f = 1/(1/do + 1/di). Plug in the known values for do and di, and solve for f. Again, make sure to use the correct units for do and di to get the focal length in the same units.

## 4. What is the significance of the focal length in the mirror equation?

The focal length is a measure of the curvature of the mirror and determines the distance at which the image of an object will be formed. It is an important factor in understanding how an image is formed by a curved mirror and can help in determining the size and orientation of the image.

## 5. Can the mirror equation be applied to all types of mirrors?

Yes, the mirror equation can be applied to all types of mirrors, including concave and convex mirrors. However, for concave mirrors, the focal length is considered negative as the mirror curves inward, while for convex mirrors, the focal length is positive as the mirror curves outward.

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