Question

find the separation between object and its image if a convex mirror of a length 20 cm forms an image which is half the size of the object​

Answer 1

Answer:

A convex mirror of radius of curvature 20 cm forms an image which is half the size of the object. Locate the position of object and its image. [Ans : -10 cm ; +5 cm]

Explanation:

Generalized spherical mirror equation:

(1 / v) + (1 / u) = (1 / f) = (2 / r)

v: image distance, u: object distance, f: focal length, r: radius of curvature

Light is assumed to be incident on the mirror from left to right.

All distances are measured from the pole of the mirror.

Distance of any point lying to the left of the pole is taken as negative and distance of any point lying to the right of the pole is taken as positive.

Object distance is always negative.

Image distance is negative for any real image and positive for any virtual image.

Focal length and radius of curvature both are negative for concave mirror. Both these are positive for convex mirror.

Magnification of an image, m = |v| / |u|.

Here, r = (+20) cm and m = 0.5.

So, |u| = 2 * |v|

We know, convex mirror always produces a virtual image; so, take v = (+x) cm. So, u = (-2x) cm.

Therefore, (1 / x) + {1 / (-2x)} = (2 / 20)

Or, (1 / 2x) = (1 / 10)

Or, x = (+5)

So, u = (-2x) cm = (-10) cm.

Therefore, object distance is 10 cm in front of the mirror.

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Answer 2

Explanation:

A convex mirror of radius of curvature 20cm forms an image which is half the size of the object. 10;+5cm .