Question

Use the mirror formula to deduce that a convex mirror always produces a virtual image of an object kept in front of it.

Hint:

In convex mirrors, the image is always virtual, upright, and diminished. The image is formed behind the mirror, and the object distance is negative. The sign conventions are crucial when applying the mirror formula.

Answer 1

The mirror formula is given by \( \frac{1}{f} = \frac{1}{v} + \frac{1}{u} \), where \( f \) is the focal length, \( u \) is the object distance, and \( v \) is the image distance.For a convex mirror:

• Focal length \( f \) is positive.
• The image formed is always virtual.

1. Object Distance \( u \): Placed in front of the mirror, \( u \) is negative by convention.2. Image Distance \( v \): Always positive and virtual, formed behind the mirror.3. Derivation: A convex mirror consistently produces a virtual, upright, and diminished image. The positive \( v \) (virtual image) and negative \( u \) (real object) ensure the mirror formula holds for virtual images.Conclusion: A convex mirror invariably forms a virtual image, regardless of the object's position.