How Do Mirrors Form Images and Affect Their Orientation?

[chase222]

I have 2 questions regarding mirrors:

If you look at yourself in a shiny Christmas tree ball with a diameter of 9.0 cm when your face is 30.0 cm away from it, where is your image? Is it real or virtual? Is it upright or inverted?

I know the mirror equation is:

(1/object distance) + (1/image distance) = 1/f
I know that the object distance is 30.0 cm, but I am confused as to what the 9.0 cm represents. Do I divide that number in half to equal 4.5, and would that number be my radius of curvature? Also I don't understand how you tell if an image is real or virtual, and upright or inverted? Is it just inverted if the number is negative?

The other problem is:

How far from a concave mirror (radius 27 cm) must an object be placed if its image is to be at infinity?

To solve this I set up the mirror equation from above, except I rearranged it to be:
(1/f) - (1/image distance) = (1/object distance)
so to plug it in it would be:
(1/13.5)-(1/infinity)=1/object distance
I got the 13.5 by dividing the radius in half. However, I don't get how to solve this problem b/c you can't plug infinity into the calculator.

Please help! Thanks!

 

[Chi Meson]

first question. the focal length of any mirror is 1/r. You have been given the diameter, so now you need 1/2 the radius.

Also, all convex mirrors are diverging mirrors, so therfre the focal lengths are defined to be negative quantities. All images in a diverging mirror will always be virtual, upright, and reduced in size.

Second question: 1/infinity = zero

 

[thepatientmental]

Regarding the first question, the 9.0 cm represents the diameter of the Christmas tree ball. In this case, it is not necessary to divide it in half. The radius of curvature would be half of the diameter, so in this case it would be 4.5 cm.

To determine if an image is real or virtual, you need to consider the sign of the image distance. A positive image distance indicates a real image, while a negative image distance indicates a virtual image. In this case, since the image distance is positive, the image would be real.

To determine if an image is upright or inverted, you need to consider the magnification. A positive magnification indicates an upright image, while a negative magnification indicates an inverted image. In this case, since the magnification is negative, the image would be inverted.

Regarding the second question, it is not possible to have an image at infinity with a concave mirror. This is because a concave mirror can only produce real images, which are always located in front of the mirror. So, there is no distance at which the image would be at infinity.

In this case, the object would need to be placed at the focal point (which is half the radius of curvature) in order to produce an image at infinity. This is because the mirror equation would become (1/27 cm) + (1/∞) = 1/f, and since 1/∞ is equal to 0, the object distance would be equal to the focal length, which is half the radius of curvature.

I hope this helps clarify your doubts about mirrors. Remember to pay attention to the signs in the equations to determine the nature and orientation of the image. Good luck with your studies!