Optics question, locate mirror and its focal length

[SlothNast]

Homework Statement

"An object 10 cm tall is placed at the zero mark of a meter stick. A spherical mirror located at some point on the meter stick creates an image of the object that is upright, 4 cm tall, and located at the 42 cm mark of the meter stick. Where is the mirror located and what is the focal length?"

Homework Equations

1/do + 1/di = 1/f

The Attempt at a Solution

 

[voko]

What have you done so far?

 

[SlothNast]

Well I've determined it must be a convex mirror, for the upright and miniature image. I have drawn a few rays from the real 10 cm object to the 4 cm image, but I am not sure how to find the location of the mirror and its focal point from that.

 

[voko]

What rays in particular have you tried? Just two rays is enough.

 

[Nickie]

To solve this problem, we can use the mirror equation which states that the inverse of the object distance (do) plus the inverse of the image distance (di) is equal to the inverse of the focal length (f). We can set up this equation as follows:

1/10 + 1/di = 1/f

We know that the image distance is 42 cm, so we can substitute that into the equation:

1/10 + 1/42 = 1/f

Solving for f, we get a focal length of 30 cm. This means that the mirror is located 30 cm away from the object, which is equivalent to the 30 cm mark on the meter stick.

Therefore, the mirror is located at the 30 cm mark on the meter stick and its focal length is 30 cm. This information can be used to determine the type of mirror (convex or concave) and the magnification of the image.