Introduction

The convex mirror formula is a fundamental concept in optics, relating object distance (u), image distance (v), and focal length (f). Mastery of this formula is essential for solving problems involving convex mirrors.

Frequently Asked Questions

1. What is the mirror formula for a convex mirror?

The mirror formula applicable to both concave and convex mirrors is:

$\frac{}{}$
1
f

=

1
u

+

1
v

2. What are the sign conventions for a convex mirror?

In the context of convex mirrors, the following sign conventions are used:

• Focal length (f): Positive, as the focal point is behind the mirror.
• Object distance (u): Negative, since the object is placed in front of the mirror.
• Image distance (v): Negative, because the image is virtual and formed behind the mirror.

3. How do I apply the mirror formula for a convex mirror?

To apply the mirror formula:

1. Assign the correct signs to u, v, and f based on the conventions above.
2. Substitute the known values into the formula.
3. Solve for the unknown variable.

4. Can you provide an example using the convex mirror formula?

Consider a convex mirror with a focal length of 10 cm (f = +10 cm) and an object placed 20 cm in front of it (u = -20 cm). Using the mirror formula:

$\frac{}{}$
1
f

=

1
u

+

1
v

Substituting the known values:

$\frac{}{}$
1
10

=

1
–
20

+

1
v

Solving for v:

$\frac{}{}$
1
v

=

1
10

–

1
–
20

$\frac{}{}$
1
v

=

1
10

+

1
20

$\frac{}{}$
1
v

=

3
20

Therefore, v = 6.67 cm.

This indicates that the image is virtual, upright, and located 6.67 cm behind the mirror.

5. Why is the focal length positive but the image distance negative in a convex mirror?

In convex mirrors, the focal length is positive because the focal point is behind the mirror, following standard sign conventions. The image distance is negative because convex mirrors form virtual images that appear to be located behind the mirror.

Derivation of the Convex Mirror Formula

The mirror formula relates the object distance (u), image distance (v), and focal length (f) of a mirror. For a convex mirror, the derivation involves geometric considerations and the application of sign conventions.

Starting with the mirror equation:

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$\frac{}{}$
1
f

=

1
u

+

1
v

$\frac{}{}$
1
f

=

1
u

+

1
v