Introduction
In this article, we will learn about the mirror formula and linear magnification in spherical mirrors. These are important concepts in the reflection of light and image formation.
Mirror Formula Definition
The mirror formula establishes a relationship between the object distance (u), the image distance (v), and the focal length (f) of a mirror.
Mirror Formula:
1/f = 1/v + 1/u
Where:
- f = focal length of the mirror
- v = image distance (measured from the mirror)
- u = object distance (measured from the mirror)
Linear Magnification
Magnification is the ratio of the height of the image to the height of the object.
Magnification Formula:
Magnification (M) = Height of Image / Height of Object = v / u
Note that the magnification can be positive or negative depending on the nature of the image (real or virtual).
Important Notes
- Use proper sign conventions (positive for distances measured to the right of the mirror, negative to the left).
- For concave mirrors, the focal length is negative.
- For convex mirrors, the focal length is positive.
- Image distance and object distance must be taken with sign according to the convention.
Example Problem
Problem: An object is placed 30 cm in front of a concave mirror with a focal length of 10 cm. Find the image distance and magnification.
Solution:
Using the mirror formula:
1/f = 1/v + 1/u
Here, f = -10 cm, u = -30 cm (since the object is in front of the mirror)
So,
1/(-10) = 1/v + 1/(-30)
-1/10 + 1/30 = 1/v
(-3 + 1)/30 = 1/v
-2/30 = 1/v ⇒ v = -15 cm
So, the image is formed 15 cm in front of the mirror (real and inverted).
Magnification: v/u = -15 / -30 = 0.5
The image is half the size of the object.
Conclusion
The mirror formula and magnification equation are fundamental to understanding image formation in curved mirrors. Practicing problems helps build clarity on these topics for academic and practical applications.
