Related Problems with Solution
Problem 1 : Convex Mirror
Problem Statement: A convex mirror has a focal length of -15 cm. An object is placed at a distance of 30 cm from the mirror. Determine the position and nature of the image formed.
Solution :
- Given: Focal length ((f)) = -15 cm, Object distance ((u)) = 30 cm.
- Use the mirror equation: $$(\frac{1}{f} = \frac{1}{v} + \frac{1}{u}).$$
- Substitute the values: $$(\frac{1}{-15} = \frac{1}{v} + \frac{1}{30}).$$
- Solve for (v): $$(v = 10 , \text{cm}).$$
- Now, use the magnification formula: $$(M = -\frac{v}{u}).$$
- Substitute the values: $$(M = -\frac{10 , \text{cm}}{30 , \text{cm}} = -\frac{1}{3}).$$ So, the image is formed at 10 cm from the mirror, on the same side as the object, and it is virtual, upright, and diminished.
