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_o = ∞, the object is at infinity and the image is formed at the focal point.
• When d_o = f, the object is at the focal point and the image is formed at infinity.
• When d_o < 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.