Despite the numerous possible projections of images when dealing with lenses and curved mirrors, there is only one equation for the location and one equation for the magnification of the image.
Location of an image
C=location of center of mirror
heavily curved mirror means smaller C
lightly curved mirror means larger C
O=location of the object
I = point where image will be formed
To derive the equation:
First, Pick a singular point on the mirror
Second, Draw two lines, one from the image's point on the horizontal axis to the point on the mirror; the other from the object's point on the hor. axis to the point on the mirror.
First, we find that: θi + θo = θf
f= the focus point or the halfway point between the centre of a mirror and the sides
θi - θo = θf
Aberations are imperfections on a mirror or lens or on the resulting images.
In reality, it is nearly impossible to construct a mirror or lens without some degree of aberration
A spherical mirror is great for images up close. However, at a great distance, the images will appear blurry with a spherical mirror.
So, astronomers use parabolic mirrors to offset this.
Another way to prevent aberations is to only allow light near the axis to go through,
Magnification of the image:
Magnification of the image is the ratio between the size of the resulting image vs. the size of the object. We can calculate this magnification by measuring the distance from the resulting image to the lens/glass (i) and measuring the distance between the lens/glass to the object (o). The sign of your 'I" value depends on whether your image is on the same side as the object or on the opposite side (if the lens is the barrier).
Your "o" value is usually positive. With this information you can calculate magnification.
M = -i/o
If the M value is negative, the image is flipped upside-down from the object's orientation. Furthermore, the resulting image is real because, as shown in Chapter 2, the rays of light meet.
If the M value is positive, the image is oriented upright and the image is virtual (the rays of light never actually meet up).