an object is placed 20cm from the convex mirror. its image is formed 12cm from the mirror. find the focal length of the mirror ?

To find the focal length of a convex mirror when you know the object distance and the image distance, you can use the mirror formula, which is given by:

Mirror Formula

The mirror formula is expressed as:

1/f = 1/v + 1/u

Where:

• f = focal length of the mirror
• v = image distance (positive for virtual images in convex mirrors)
• u = object distance (negative as per sign convention)

Given Values

In this case, the object distance (u) is -20 cm (negative because it is measured against the direction of the incoming light), and the image distance (v) is +12 cm (positive because the image formed by a convex mirror is virtual and located behind the mirror).

Substituting Values into the Formula

Now, we can substitute these values into the mirror formula:

1/f = 1/v + 1/u

Substituting the known values:

1/f = 1/12 + 1/(-20)

Calculating Each Term

First, calculate the right side of the equation:

1/f = 1/12 - 1/20

To combine these fractions, we need a common denominator. The least common multiple of 12 and 20 is 60:

• 1/12 = 5/60
• 1/20 = 3/60

Now, substituting these values gives:

1/f = 5/60 - 3/60 = 2/60

Finding the Focal Length

Now, simplify the fraction:

1/f = 1/30

To find the focal length (f), take the reciprocal:

f = 30 cm

Final Result

The focal length of the convex mirror is +30 cm. The positive sign indicates that it is a convex mirror, which is consistent with the properties of such mirrors.