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MIRROR FORMULA
In a spherical mirror, the distance of the object from its pole is called the object distance (u).
The distance of the image from the pole of the mirror is called the image distance (v).
The distance of the principal focus from the pole is called the focal length (f).
There is a relationship between these three quantities given by the mirror formula which is expressed as-
Sign Convention for Reflection by Spherical Mirrors
While dealing with the reflection of light by spherical mirrors, we shall follow a set of sign conventions called the New Cartesian Sign Convention. In this convention, the pole (P) of the mirror is taken as the origin. The principal axis of the mirror is taken as the x-axis (X’X) of the coordinate system. The conventions are as follows –
(i)The object is always placed to the left of the mirror. This implies that the light from the object falls on the mirror from the left-hand side.
(ii) All distances parallel to the principal axis are measured from the pole of the mirror.
(iii)All the distances measured to the right of the origin (along + x-axis) are taken as positive while those measured to the left of the origin (along – x-axis) are taken as negative.
(iv)Distances measured perpendicular to and above the principal axis (along + y-axis) are taken as positive.
(v)Distances measured perpendicular to and below the principal axis (along –y-axis) are taken as negative.
Questions related to it-
Q.1 A convex mirror used for rear-view on an automobile has a radius of curvature of 3.00 m. If a bus is located at 5.00 m from this mirror, find the position, nature and size of the image.
Solution-
Q.2 The image formed by a concave mirror is observed to be virtual, erect and larger than the object. Where should be the position of the object?
(a)Between the principal focus and the centre of curvature
(b) At the centre of curvature
(c) Beyond the centre of curvature
(d) Between the pole of the mirror and its principal focus.
Ans D
Q.3 No matter how far you stand from a mirror, your image appears erect. The mirror is likely to be:
(a)plane.
(b)concave.
(c)convex.
(d)either plane or convex.
Ans D
Q.4 A concave mirror produces three times magnified (enlarged) real image of an object placed at 10 cm in front of it. Where is the image located?
Solution:
Let the height of the object= h
Then,the height of the image= -3h (real image)
m= -3h/h = -v/u
v/u will be 3
As, u = -10cm (given)
v = 3 x (-10) = -30cm
Hence, an inverted image is formed at a distance of 30cm in front of the given concave mirror.
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