The Mirror Equationray Optics And Optical Instruments
The Mirror Equation:
Equation:
$$ \frac{1}{d_o} + \frac{1}{d_i} = \frac{1}{f}$$
- do is the distance between the object and the mirror.
- di is the distance between the image and the mirror.
- f is the focal length of the mirror.
Sign Conventions:
- do is positive when the object is in front of the mirror.
- di is positive when the image is in front of the mirror.
- f is positive for a concave mirror and negative for a convex mirror.
Magnification:
Equation:
$$ M = \frac{h_i}{h_o} = -\frac{d_i}{d_o}$$
- M is the magnification of the image.
- hi is the height of the image.
- ho is the height of the object.
Special Cases:
- When do = ∞, the object is at infinity and the image is formed at the focal point.
- When do = f, the object is at the focal point and the image is formed at infinity.
- When do < f, the object is between the focal point and the mirror and the image is formed behind the mirror.
Applications of the Mirror Equation:
- Determining the focal length of a mirror.
- Finding the image distance for a given object distance.
- Calculating the magnification of an image.
