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Concave mirrors

Concave mirrors have a focal point. All light that is parallel to the axis of the mirror will be reflected according to the Law of Reflection through this focal point. Conversely, a point source of light (such as a bulb) placed at the focal point, will project rays towards all points on the mirror, which then reflect out parallel to the axis of the concave mirror.

Torches, flashlights, searchlights, and so on, are examples of concave mirrors.

The image

The object distance ($d_o$) is the distance from the object to the mirror surface, and $d_i$ is the distance from the mirror to the image. The distance from the image to the focal point (F) is the focal length f. The ratios of these distances follow this rule:

$$1/{d_o} + 1/{d_i} = 1/f$$

After the parallel rays from the object have been reflected through the focal point, they form an image. For an object far from the mirror, this image is inverted, small, and real. Remember, a real image is one which the light rays really pass through.

As the object comes closer to the mirror, the image moves away from the mirror and grows larger.

Concave mirror
For an object far from the mirror, the image formed is inverted, small, and real
Concave mirror
When the object is at the centre of curvature (C) the object and image are the same size, with the image inverted
Concave mirror
As the object moves between C and F (focal point), the image is larger than the object, inverted and further away than C
Concave mirror
When the object is at F, the lines of the image from the mirror are parallel, and do not form an image at all

When the object is between F and the mirror, the image is virtual, upright, and enlarged.

Convave mirror virtual image
Concave mirrors form virtual, upright and enlarged images when the object is between the mirror and the focal point

Magnification

The magnification, M, in a concave mirror, is the ratio of the height of the image, $h_i$, and the height of the object, $h_o$:

$$M = {h_i}/{h_o}$$

The magnification is also the ratio of the image-mirror distance, $d_i$, and object-mirror distance, $d_o$:

$$M = {d_i}/{d_o}$$

Content © Andrew Bone. All rights reserved. Created : March 5, 2014

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