optics

Mirror Equations of Curved Mirrors
We use the given picture below to derive the equations of concave and convex mirrors.

While deriving equations we use the similarities of triangles given picture above. We show them with red lines in the picture. I do not want to make confusion in your mind and write down the equations that I get from similarity of two triangles.

In this equation, we take the quantities positive if they in front of the mirror. In other words, if the object, image and focal point of the mirror are located in front of the mirror (like concave mirrors) we take them positive; if they are located behind the mirror (like convex mirrors) we take them as negative. In convex mirrors focal length is taken as negative since it is behind the mirror and in concave mirrors if the image is behind the mirror then we take it also as negative.
Mirror Equations of Curved Mirrors
We use the given picture below to derive the equations of concave and convex mirrors.

While deriving equations we use the similarities of triangles given picture above. We show them with red lines in the picture. I do not want to make confusion in your mind and write down the equations that I get from similarity of two triangles.

In this equation, we take the quantities positive if they in front of the mirror. In other words, if the object, image and focal point of the mirror are located in front of the mirror (like concave mirrors) we take them positive; if they are located behind the mirror (like convex mirrors) we take them as negative. In convex mirrors focal length is taken as negative since it is behind the mirror and in concave mirrors if the image is behind the mirror then we take it also as negative.