Plane mirror problems
Understanding Plane Mirror Problems
Plane mirrors are flat mirrors that reflect light according to the law of reflection. When dealing with plane mirror problems, it's essential to understand the basic principles of image formation and the characteristics of the images produced by plane mirrors. In this in-depth guide, we will explore the key concepts, formulas, and examples to help you understand and solve plane mirror problems effectively.
Key Concepts
Law of Reflection
The law of reflection states that the angle of incidence (the angle between the incident ray and the normal to the surface) is equal to the angle of reflection (the angle between the reflected ray and the normal).
$$ \theta_{\text{incidence}} = \theta_{\text{reflection}} $$
Image Formation
In a plane mirror, the image formed is always virtual, upright, and of the same size as the object. The image is as far behind the mirror as the object is in front of it.
Characteristics of Images Formed by Plane Mirrors
| Characteristic | Description |
|---|---|
| Nature | Virtual and erect |
| Size | Same as the object |
| Orientation | Laterally inverted |
| Distance | Equal to the distance of the object from the mirror |
| Number of Images | One image per mirror |
Formulas and Principles
Image Distance
The distance of the image from the mirror ($d_{\text{image}}$) is equal to the distance of the object from the mirror ($d_{\text{object}}$).
$$ d_{\text{image}} = d_{\text{object}} $$
Lateral Magnification
The lateral magnification ($M$) for a plane mirror is always +1, indicating that the image is the same size as the object.
$$ M = \frac{h_{\text{image}}}{h_{\text{object}}} = +1 $$
where $h_{\text{image}}$ is the height of the image and $h_{\text{object}}$ is the height of the object.
Multiple Plane Mirrors
When multiple plane mirrors are used, the number of images formed can be calculated using the formula:
$$ N = 360^\circ / \theta - 1 $$
where $N$ is the number of images and $\theta$ is the angle between the mirrors.
Examples
Example 1: Image Formation
Problem: An object is placed 10 cm in front of a plane mirror. Where is the image formed, and what are its characteristics?
Solution:
- Image distance ($d_{\text{image}}$) = Object distance ($d_{\text{object}}$) = 10 cm
- The image is virtual, erect, and laterally inverted.
- The image size is the same as the object size.
Example 2: Multiple Plane Mirrors
Problem: Two plane mirrors are placed at a 90-degree angle to each other. How many images will be formed if an object is placed between them?
Solution: Using the formula for multiple plane mirrors:
$$ N = 360^\circ / \theta - 1 $$ $$ N = 360^\circ / 90^\circ - 1 $$ $$ N = 4 - 1 $$ $$ N = 3 $$
Three images will be formed.
Example 3: Lateral Magnification
Problem: An object 5 cm tall is placed in front of a plane mirror. Calculate the height of the image.
Solution: Since the lateral magnification ($M$) for a plane mirror is +1:
$$ h_{\text{image}} = M \cdot h_{\text{object}} $$ $$ h_{\text{image}} = +1 \cdot 5 \text{ cm} $$ $$ h_{\text{image}} = 5 \text{ cm} $$
The height of the image is 5 cm, which is the same as the object's height.
Conclusion
Understanding plane mirror problems requires a grasp of the law of reflection, image formation, and the characteristics of images produced by plane mirrors. By applying the principles and formulas discussed above, you can solve a wide range of problems involving plane mirrors. Remember that practice is key to mastering these concepts, so be sure to work through various examples and problems to reinforce your understanding.