Spherical Mirrors

Spherical mirrors are mirrors of curved shape. There are two types of spherical mirror – concave and convex. The image formed in these types of mirror differs from the image formed in a plane mirror. Before we discuss the formation of image in each type, we familiarize first the following terms and symbols that we will encounter in the discussion.

C – center of curvature

c – central axis

V – center of the spherical section

Principal axis – line through C and V

F – focal point

f – focal length

O – symbol for object

I – symbol for image

P – distance from the object to the mirror

q – distance of image from the mirror

CONCAVE MIRRORS

Concave Mirrors are those in which the reflection of light is from the inner, concave surface of the spherical mirror. From its name, concave, it curves inward like a cave. Here are some properties of a concave mirror:

1. The radius of curvature in a concave mirror is a positive quantity.
2. If parallel rays pass through a concave mirror parallel to the central axis, the reflected rays pass through a common point called focus at a distance called focal length from the mirror.
3. The focal point of a concave mirror is said to be a real focal point and the focal length is a positive quantity.
4. In spherical mirrors, the focal length is half the radius of curvature, and the radius of curvature in a concave mirror is positive.
5. The image formed in a concave mirror can be real or virtual, depending on the position of the object from the focal point, if its inside, outside or at the focal point.

To locate the focal point in a concave mirror, draw rays of light towards the mirror parallel to the central axis. These rays are reflected and tend to converge to a common point and this is called the focal point, F. the distance from the focal point to the mirror is the focal length, f. As shown in the figure, F is located between the center of curvature and the mirror and the focal length is half the radius of curvature.

To make a ray diagram for concave mirrors, we follow these steps. The list contains three types of rays to be drawn to locate the image formed and see what type of image is formed in a concave mirror.

1. Ray 1 – Draw a ray, from the top of the object, parallel to the principal axis, to the mirror then reflect with the ray passing through the focal point.
2. Ray 2 – Ray passing through the focal point, to the mirror, and is reflected parallel to the principal axis.
3. Ray 3 – Ray passing through the center of curvature and reflected back to itself.

The following figures show the image formed in a concave mirror at different object position.

1. When the object is inside the focal point.
1. Place the object, O between the focal point and the mirror.
2. Draw ray 1, 2, and 3.
3. The point where the rays converge is where the image is located. Always draw the image from the principal axis to the converging point. 1. When the object is at the focal point.
1. Place the object at the focal point.
2. Draw ray 1, 2, and 3.
3. The point where the rays converge is where the image is located. Always draw the image from the principal axis to the converging point. 1. When the object is outside the focal point.
1. Place the object, O between the center of curvature and the focal point.
2. Draw ray 1, 2, and 3.
3. The point where the rays converge is where the image is located. Always draw the image from the principal axis to the converging point. CONVEX MIRRORS

A convex mirror which is sometimes called a diverging mirror so because the rays from any point on an object tends to separate or diverge after reflection making them like coming from some point behind the mirror. The properties of a convex mirror are as follows:

1. the radius of curvature is a negative quantity;
2. if parallel rays are sent a convex mirror, backward extensions of the reflected rays pass through a common point or the focus at a distance from the mirror;
3. the focus is virtual and the focal length is a negative quantity;
4. the only image formed is virtual.