Question

Based on the given data, determine the image position formed by a spherical mirror: \[ u = -20\, \text{cm}, f = -15\, \text{cm} \]

Hint:

Use sign convention carefully in mirror formula: Real images have negative v, virtual images have positive v for concave mirrors.

Answer 1

Using the mirror formula: \[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \] Substituting values: \[ \frac{1}{-15} = \frac{1}{v} - \frac{1}{-20} \Rightarrow \frac{1}{v} = \frac{1}{-15} + \frac{1}{20} \] \[ \frac{1}{v} = \frac{-4 + 3}{60} = \frac{-1}{60} \Rightarrow v = -60\, \text{cm} \] Thus, the image is formed 60 cm in front of the mirror.
Since $v$ is negative:
The image is real and inverted.
It lies beyond the center of curvature.