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Transcript

Curved Mirrors

Reflecting Light

Light usually travels in straight lines. It changes direction if it hits a shiny surface, or if it travels from one material into another. This change in direction at a shiny surface such as a mirror is called reflection.

Reflecting Light

Looking in the mirror

When you look in a mirror, rays of light from your face reflect off the shiny surface and back to your eyes. You seem to see an image of yourself behind the mirror. To understand why this is, we need to use the law of reflection of light.

When a ray of light reflects off a mirror or other reflecting surfaces, it follows a path. The ray bounces off, rather like a ball bouncing off a wall. The two rays are known as the incident ray and the reflected ray. The angle of incidence i and the angle of reflection r are found to be equal to each other. This is the law of reflection, which can be written as follows:

angle of incidence = angle of reflection

i = r

Note that, to find the angles i and r, we have to draw the normal to the reflecting surface. This is a line drawn perpendicular (at 90°) to the surface, at the point where the ray strikes it. The other two angles (between the rays and the flat surface) are also equal. However, we would have trouble measuring these angles if the surface was curved, so we measure the angles relative to the normal.

Plane Mirrors

The image shows how an observer can see an image of a candle in a plane mirror. Light rays from the flame are reflected by the mirror. Some of them enter the observer's eye. In the diagram, the observer has to look forward and slightly to the left to see the image of the candle. Their brain assumes that the image of the candle is in that direction, as shown by the dashed lines behind the mirror. Our brains assume that light travels in straight lines, even though we know that light is reflected by mirrors.

When an object is reflected in a plane mirror, its image is:

  • the same distance behind the mirror as the object is in front of it
  • the same size as the object
  • left-right inverted
  • virtual

Plane Mirrors

Same Distance

The dashed lines appear to be coming from a point behind the mirror, at the same distance behind the mirror as the candle is in front of it. You can see this from the symmetry of the diagram.

Same Size

The image looks as though it is the same size as the candle.

Left-Right Inverted

It is a mirror image, that is, it is left-right reversed or inverted. You will know this from seeing writing reflected in a mirror. If you could place the object and its image side-by-side, you would see that they are mirror images of each other, in the same way that your left and right hands are mirror images of each other.

Virtual

The image of the candle in the mirror is not a real image. A real image is an image that can be formed on a screen. If you place a piece of paper at the position of the image, you will not see a picture of the candle on it, because no rays of light from the candle reach that spot. That is why we drew dashed lines, to show where the rays appear to be coming from. We say that it is a virtual image.

Curved Mirrors

We will now turn our attention to the topic of curved mirrors, and specifically curved mirrors that have a spherical shape. Such mirrors are called spherical mirrors. The two types of spherical mirrors are shown in the diagram on the right; concave mirrors and convex mirrors. Spherical mirrors can be thought of as a portion of a sphere that was sliced away and then silvered on one of the sides to form a reflecting surface. Concave mirrors were silvered on the inside of the sphere and convex mirrors were silvered on the outside of the sphere.

Curved Mirrors

Concave Mirrors

Ray Diagrams

Principal Axis

If a concave mirror were thought of as being a slice of a sphere, then there would be a line passing through the center of the sphere and attaching to the mirror at its exact center. This line is known as the principal axis.

Center of Curvature

The point in the center of the sphere from which the mirror was sliced is known as the center of curvature and is denoted by the letter C in the diagram on the right.

Vertex

The point on the mirror's surface where the principal axis meets the mirror is known as the vertex and is denoted by the letter A in the diagram below. The vertex is the geometric center of the mirror.

Focal Point

Midway between the vertex and the center of curvature is a point known as the focal point; the focal point is denoted by the letter F in the diagram below.

Radius of Curvature

The distance from the vertex to the center of curvature is known as the radius of curvature (represented by R). The radius of curvature is the radius of the sphere from which the mirror was cut.

Focal Length

Finally, the distance from the mirror to the focal point is known as the focal length (represented by F). Since the focal point is the midpoint of the line segment adjoining the vertex and the center of curvature, the focal length would be one-half the radius of curvature.

Concave Mirrors

Properties

  • Concave mirror refers to the mirror whose reflecting surface is towards the center of curvature
  • Center of curvature lies in front of the mirror
  • Converging mirror
  • Real or virtual image is formed
  • Used as reflectors in projectors, searchlights etc.

It can reflect images in two ways:

  • When the object is closer to the mirror, the image formed will appear larger and right side up, i.e. a virtual image is formed.
  • When the object is farther away to the mirror, the image formed will appear small, and upside down, i.e. a real image is formed.

Convex Mirrors

Ray Diagrams

The center of that original sphere is known as the center of curvature (C) and the line that passes from the mirror's surface through the sphere's center is known as the principal axis. The mirror has a focal point (F) that is located along the principal axis, midway between the mirror's surface and the center of curvature.

Note that the center of curvature and the focal point are located on the side of the mirror opposite the object - behind the mirror. Since the focal point is located behind the convex mirror, such a mirror is said to have a negative focal length value.

A convex mirror is sometimes referred to as a diverging mirror due to the fact that incident light originating from the same point and will reflect off the mirror surface and diverge.

After reflection, the light rays diverge; subsequently they will never intersect on the object side of the mirror. For this reason, convex mirrors produce virtual images that are located somewhere behind the mirror.

Convex Mirrors

Properties

  • Convex mirror implies the mirror whose reflecting surface is away from the center of curvature.
  • Center of curvature lies behind the mirror
  • Diverging mirror
  • Virtual image is formed
  • Used as rear view mirrors in cars and bikes
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