# What is the mirror's focal length?

• jaejoon89
In summary, a concave mirror can create an image on the screen 2x larger than the object. To achieve an image 3x larger, both the object and screen are moved. If the screen is moved 0.75 m, then the object must also be moved. Additionally, the mirror's focal length can be found using the equations M = h_i / h_o = - d_i / d_o and 1/f = 1/d_o + 1/d_i, where i refers to image and o refers to object. With this information, it is possible to find any unknowns by setting up 4 equations and 4 unknowns.
jaejoon89
A concave mirror creates an image on the screen 2x larger than the object. Both objects and screen are subsequently moved in order to create an image on the screen 3x larger than the object. 1) If the screen is moved 0.75 m in this process, how far is the object also moved? 2) What is the mirror's focal length?

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I think the equations are:
1) M = h_i / h_o = - d_i / d_o
2) 1/f = 1/d_o + 1/d_i
where i refers to image, o refers to object

I'm really not sure how to set this up.

You could try putting the given information into the two formulas.
Repeat for the situation after moving the screen and object.
Looks like 4 equations and 4 unknowns, so you should be able to find anything you want!

Can you provide more information about the setup and the values of the variables? Are we assuming the object is at the focal point of the mirror at the beginning? Also, are we assuming the mirror is a perfect concave mirror with no distortion? This information will help me provide a more accurate response.

## What is the mirror's focal length?

The mirror's focal length is the distance from the center of the mirror to the focal point, where parallel light rays converge after reflecting off the mirror.

## How is the mirror's focal length calculated?

The mirror's focal length can be calculated using the formula: F = R/2, where F is the focal length and R is the radius of curvature of the mirror.

## What is the difference between a convex and concave mirror's focal length?

A convex mirror's focal length is positive, meaning the focal point is in front of the mirror, while a concave mirror's focal length is negative, meaning the focal point is behind the mirror.

## Can the mirror's focal length be changed?

Yes, the mirror's focal length can be changed by adjusting the curvature of the mirror's surface or by using a lens in front of the mirror.

## What is the significance of knowing the mirror's focal length?

Knowing the mirror's focal length is important in understanding how light will reflect off the mirror and where an image will be formed. It is also essential in designing optical instruments such as telescopes and cameras.

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