Section 6.4: Mirrors

Mirrors are reflective surfaces that form images. The main types are:

  • Plane Mirrors: Form virtual, upright images equal in size to the object.
  • Concave Mirrors: Converging mirrors; can form real or virtual images depending on object distance.
  • Convex Mirrors: Diverging mirrors; always form virtual, upright, and reduced images.

Mirror formula relates object distance (\(u\)), image distance (\(v\)), and focal length (\(f\)): \[ \frac{1}{f} = \frac{1}{v} + \frac{1}{u} \] Magnification: \( m = -\frac{v}{u} \)

Example: Image Formation by a Concave Mirror

An object is placed 15 cm in front of a concave mirror of focal length 10 cm. Find the image distance and magnification.

Using the mirror formula: \( \frac{1}{f} = \frac{1}{u} + \frac{1}{v} \) \( \frac{1}{10} = \frac{1}{15} + \frac{1}{v} \) → \( \frac{1}{v} = \frac{1}{10} - \frac{1}{15} = \frac{1}{30} \) → \( v = 30\,\text{cm} \) Magnification: \( m = -\frac{v}{u} = -\frac{30}{15} = -2 \) (image is real, inverted, and magnified)

Practice Problems

  1. A plane mirror is placed 20 cm from an object. Find the image distance.
  2. An object is 25 cm from a convex mirror with focal length 15 cm. Determine the image distance and magnification.
  3. A concave mirror has focal length 12 cm. An object is placed 18 cm away. Find the image location and size.
  4. Draw ray diagrams for concave mirrors for objects beyond 2f, at 2f, and between f and 2f.
  5. Explain why convex mirrors are used as rear-view mirrors in vehicles.
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