How to solve for distance of object with a concave mirror?

In summary, to solve for the object's distance in front of a concave mirror with a radius of curvature r = 6 cm and a resulting image magnification of M = 4.3, we can rearrange the magnification equation and substitute it into the spherical mirror equation. By solving for 1/di and plugging it into the second equation, we can then solve for do using the given values of radius and magnification.
  • #1
AngelLegs
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Homework Statement


An object is placed a distance do in front of a concave mirror with a radius of curvature r = 6 cm. The image formed has a magnification of M = 4.3. Solve for the object's distance.

Homework Equations


M = -di/do
(1/do) + (1/di) = 2/R = 1/f

The Attempt at a Solution


I've tried to rearrange the magnification equation and sub it into the spherical mirror equation in order to cancel out the di's, so I can solve for do using radius and magnification, except I'm still not even entirely sure how you would manage to make this work.
How would I rearrange these equations to solve for do?
 
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  • #2
Have you tried solving for 1/di? I mean, find that in the first equation and plug it in the second. From there it should be easy.
 

1. How do I find the focal length of a concave mirror?

The focal length of a concave mirror can be found by using the formula f = R/2, where f is the focal length and R is the radius of curvature of the mirror. The radius of curvature can be measured by placing the mirror on a flat surface and measuring the distance from the center of the mirror to the surface.

2. Can I use the same formula to find the distance of an object from the concave mirror?

No, the formula for finding the distance of an object from a concave mirror is different. It is given by the equation 1/f = 1/di + 1/do, where f is the focal length, di is the distance of the image from the mirror, and do is the distance of the object from the mirror.

3. How do I determine if the image formed by a concave mirror is real or virtual?

If the distance of the object from the mirror is greater than the focal length, the image formed will be real and inverted. If the distance of the object is less than the focal length, the image formed will be virtual and upright.

4. Can I use the same formula for a concave mirror with a different shape, such as elliptical or parabolic?

No, the formula for finding the distance of an object from a concave mirror only applies to spherical mirrors. For mirrors with a different shape, the formula will need to be modified accordingly.

5. How does the distance of the object from the mirror affect the size of the image formed?

The distance of the object from the mirror does not directly affect the size of the image formed. However, the closer the object is to the mirror, the larger the image will appear. This is because the closer the object is, the larger the angle of incidence, resulting in a larger angle of reflection and therefore a larger image.

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