Solve for Image Location and Magnification in Concave Mirror | Homework Help

[Jonah14]

Homework Statement

"An object is 4.0 cm in front of a concave mirror having a 12.0-cm radius. Locate the image using the mirror equation and a ray diagram."

Homework Equations

1/f = 1/do + 1/di where f = Focal Length, do = Distance Object, di = Distance Image

m = hi/ho = -di/do where m = Magnification, hi = Height of Image, ho = Height of Object

The Attempt at a Solution

f = 6 cm
do = 4.0 cm
Ho = ?
di = -12
Hi = ?
C = 12



I got 1/6 = 1/di + 1/4
1/6 - 1/4 = 1/di
Which equaled -12


Hi/Ho = -(-12)/4
Usually I knew Hi or Ho to get the answer but I don't know it this time!
Can anyone help me with this seemingly easy problem?

 

[ordirules]

First of all, you found the answer, you just need d this time and show where it is.

Now then also probably want a diagram there, just to test your understanding of the geometry of the problem.

Ok, first of all you need to find the image, so you need to draw your ray diagram.

I wish I could post an image for this, but physicsforums won't let me (you can only link to one), which is a little lame.

But if you draw a concave mirror, then the focal point, where will be the image compared to it?

Then draw the image as a perpendicular arrow going up (your book must show this somewhere). Now you just need to draw three rays:
1. Draw a ray going straight to the mirror from the top of the arrow you drew (perpendicular to the arrow you drew as well). The rule of this ray is that it will bounce to the focal point, so when it hits the mirror, draw a straight line from there to the focal point


2. Draw a ray that goes from the top of the arrow through the focal point of the mirrror. The rule for this ray is that once it hits the mirror, it bounces back parrallel to the ground.

3. Draw a ray that goes from the top of the arrow you drew again, but this time going to the center of the mirror. The rule for this one is that you draw a line coming back at the same angle is came in, but downwards


With these three lines you have, elongate them until they intersect. They may intersect in front of or behind the mirror, so you must elongate them both ways. Where they intersect is the top part of the new arrow you will draw perpendicular to the ground, your image.

Aah, I'll just draw an example which will be simpler. Use this as a guideline to solve yours.

And now, for your problem, where is the image located, is it contestant #1, #2, #3?

 

[tomcue]

I would first commend the student for attempting to use the appropriate equations and for recognizing that they are missing some information in order to solve the problem. I would then provide the following response:

It seems like you are on the right track with your equations. In order to solve for the image location and magnification, you will need to know either the height of the object or the height of the image. This information can be obtained by drawing a ray diagram, which will show the path of light rays as they reflect off the concave mirror. By tracing the rays and measuring the distances, you can determine the height of the image or the height of the object.

Once you have this missing information, you can plug it into your equations and solve for the image location and magnification. Remember to pay attention to the signs of the distances, as they can determine whether the image is real or virtual and upright or inverted.

In addition, it is always a good idea to double check your calculations and make sure your final answer makes sense. For example, the image location should be a negative value since it is located behind the mirror, and the magnification should be a negative value if the image is inverted.

I hope this helps. Keep up the good work in using scientific principles to solve problems!