### The Mirror Equationray Optics And Optical Instruments

**The Mirror Equation:**

**Equation:**

$$ \frac{1}{d_o} + \frac{1}{d_i} = \frac{1}{f}$$

- d
_{o}is the distance between the object and the mirror. - d
_{i}is the distance between the image and the mirror. - f is the focal length of the mirror.

**Sign Conventions:**

- d
_{o}is positive when the object is in front of the mirror. - d
_{i}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.
- h
_{i}is the height of the image. - h
_{o}is the height of the object.

**Special Cases:**

**When d**the object is at infinity and the image is formed at the focal point._{o}= ∞,**When d**the object is at the focal point and the image is formed at infinity._{o}= f,**When d**the object is between the focal point and the mirror and the image is formed behind the mirror._{o}< f,

**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.