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# Sign Convention ,Mirror Formula and Magnification for Mirrors

### Sign convention of reflection of spherical mirror

1. All distances are measured from the pole.
2. Distances measured in the same direction of the incident ray are taken as positive and the distances measured in the direction opposite to the incident ray are taken as negative.
3. Perpendicular distances (height) above the principal axis are positive and perpendicular distance below the principal axis are negative thus focal length and radius of curvature is negative for concave mirror and positive for convex mirror.

The relation between object distance, image distance and the focal length for a mirror is

• The ratio of the height of image to the height of object is known as linear magnification
• The height (h2) of a virtual image will be positive.
• The height (h2) of a real image will be negative

• The linear magnification produced by a mirror is equal to the ratio of the image distance to the object distance, with a minus sign

Practice Questions

1. Find the size, nature and position of image formed when an object of size 1 cm is placed at a distance of 15 cm from a concave mirror of focal length 10 cm.
2. An object 2 cm high is placed at a distance of 16 cm from a concave mirror which produces a real image 3 cm high.
(i) What is the focal length of the mirror ?|
(ii) Find the position of the image.
3. An object 5 cm high is placed at a distance of 10 cm from a convex mirror of radius of curvature 30cm.  Find the nature and the size of the image.
4. An object, 4.0 cm in size, is placed at 25.0 cm in front of a concave mirror of focal length 15.0 cm. At what distance from the mirror should a screen be placed in order to obtain a sharp image?
Find the nature, position and size of the image.
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