The mirror formula is a mathematical relationship that describes the relationship between the object distance (u), image distance (v), and focal length (f) of a spherical mirror.
Understanding the Formula
The mirror formula is expressed as:
1/f = 1/v + 1/u
Where:
- f is the focal length of the mirror.
- u is the distance of the object from the mirror.
- v is the distance of the image from the mirror.
Sign Conventions
To use the mirror formula correctly, we need to follow certain sign conventions:
- Focal length (f): Positive for concave mirrors and negative for convex mirrors.
- Object distance (u): Always negative for real objects.
- Image distance (v): Positive for real images and negative for virtual images.
Applications of the Mirror Formula
The mirror formula is widely used in:
- Designing optical instruments: It helps calculate the position and nature of images formed by mirrors in various optical instruments like telescopes, microscopes, and cameras.
- Understanding mirror properties: It allows us to determine the focal length of a mirror if we know the object and image distances.
- Solving problems related to reflection: It can be used to solve problems involving the reflection of light from curved mirrors.
Examples
Here are a few examples of how the mirror formula is used:
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Finding the image distance: If a 5 cm tall object is placed 20 cm away from a concave mirror with a focal length of 10 cm, we can use the mirror formula to find the image distance:
- 1/10 = 1/v + 1/-20
- Solving for v, we get v = 6.67 cm. This positive value indicates that the image is real.
-
Determining the focal length: If an object placed 15 cm away from a mirror forms a real image at 30 cm, we can calculate the focal length:
- 1/f = 1/30 + 1/-15
- Solving for f, we get f = -10 cm. The negative sign indicates a convex mirror.
Conclusion
The mirror formula is a fundamental concept in optics that helps us understand the behavior of light reflected from spherical mirrors. It provides a simple yet powerful tool for calculating the image distance, object distance, and focal length of a mirror.
