Calculating Rearview Mirror + Amusement Park Mirror Images

[chase222]

I have 2 questions:
What type and height of image would a rearview mirror produce of a car that was 1.3 m high and 15.0 m behind you, assuming the mirror's radius of curvature is 3.2 m?

I don't know what equation to use to solve the problem. I think it might be:
(1/object distance) + (1/image distance) = 1/f

However, w/ this equation I don't know where to plug in the height (1.3 m). Please help!

The other question is:
A mirror at an amusement park shows an upright image of any person who stands 1.3 m in front of it. If the image is three times the person's height, what is the radius of curvature?

However, I don't understand how to solve it if we don't know how big the image is. I also know that f=r/2, which I might need later on in the problem.

Thanks!

 

[Chi Meson]

You noticed that f = r/2. You need this for the first question along with the knowledge that the sideview mirror on a car is a diverging mirror. THis means that the focal length must have a negative sign. You have the correct equation, just remember to use a negative focal length.

There is also the magnification equation which says (h_image / h_object) = (d-image / d_object). You might find this useful for both questions.

And only a diverging mirror (positive focal length) can create an upright AND larger image.

 

[thepatientmental]

For the first question, you are correct in using the equation (1/object distance) + (1/image distance) = 1/f. The height of the object (car) is not needed in this equation. Instead, you will need to know the distance of the object from the mirror (15.0 m) and the radius of curvature (3.2 m). You can then solve for the image distance, which will give you the height of the image produced by the rearview mirror.

For the second question, you are correct in using the equation f=r/2. You will also need to use the equation (1/object distance) + (1/image distance) = 1/f. The height of the image is given as three times the person's height, so you can plug in 3.9 m (1.3 m x 3) for the image distance. You can then solve for the object distance, which will give you the distance of the person from the mirror. Once you have both the object distance and the image distance, you can use the equation f=r/2 to solve for the radius of curvature. Hope this helps!