An object is placed at 3.6 m in front of a convex mirror of focal length 1.2 m. Following New Cartesian Sign Convention, the image formed at v = _______.

The correct answer is -0.9 m.

Key Points

• Convex mirrors form virtual, erect, and diminished images irrespective of the position of the object.
• The mirror formula $\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$ is used to find the image distance $v$ .
• For a convex mirror, the focal length $f$ is taken as positive according to the New Cartesian Sign Convention.
• Given: Object distance $u = -3.6$ m (object is placed in front of the mirror), focal length $f = 1.2$ m.
• Using the mirror formula: $\frac{1}{1.2} = \frac{1}{v} + \frac{1}{-3.6}$ , solving gives $v = -0.9$ m.

Additional Information

• New Cartesian Sign Convention: In this convention, distances measured in the direction of the incident light (towards the mirror) are taken as negative, while those measured in the opposite direction are positive.
• Convex Mirror: A mirror with a reflecting surface that bulges outward, causing parallel rays to diverge.
• Focal Length: The distance between the mirror's surface and its focal point. Positive for convex mirrors and negative for concave mirrors.
• Virtual Image: An image formed by a mirror or lens that cannot be projected on a screen because the light rays do not actually converge at the image location.
• Mirror Formula: An equation that relates the object distance (u), image distance (v), and focal length (f) of a mirror: $\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$ .