Playing With Spherical Mirrors

Key Notes :

Spherical Mirrors

Introduction to Spherical Mirrors:

• Spherical mirrors are curved mirrors with either a concave or convex shape.
• They have a reflective surface on the inside (concave) or outside (convex) of a sphere.

Types of Spherical Mirrors:

1. Concave Mirror:
   • Curved inward like the inside of a spoon.
   • Reflects light inwards towards a focal point.
   • Used in things like makeup mirrors and telescopes.
2. Convex Mirror:
   • Curved outward like the back of a spoon.
   • Diverges or spreads out light.
   • Commonly found in car side-view mirrors to provide a wider field of view.

Terminology:

• Center of Curvature (C): The center of the sphere from which the mirror is cut.
• Focal Point (F): The point where all parallel rays either converge (concave) or appear to diverge (convex) after reflecting.
• Principal Axis: The imaginary line passing through the center of curvature and the midpoint of the mirror.
• Aperture: The diameter of the mirror.

Reflection Rules:

1. Concave Mirror:
   • Rays parallel to the principal axis converge at the focal point (F).
   • Rays passing through the focal point (F) become parallel after reflection.
   • Rays passing through the center of curvature (C) reflect back on themselves.
2. Convex Mirror:
   • Rays parallel to the principal axis appear to diverge from the focal point (F) behind the mirror.
   • Rays diverging from the focal point (F) appear parallel after reflection.
   • Rays that strike the mirror reflect outward.

Image Formation:

• Concave Mirror:
  • Real and inverted image when the object is beyond the focal point (F).
  • Virtual and upright image when the object is between the focal point (F) and the mirror.
• Convex Mirror:
  • Always forms a virtual, smaller, and upright image, regardless of the object’s position.

Mirror Equations:

• Concave Mirror:
  • The mirror equation is 1/f = 1/v + 1/u, where:
    • f is the focal length.
    • v is the image distance.
    • u is the object distance.
• Convex Mirror:
  • For convex mirrors, the focal length (f) is negative.

Magnification (m):

• Magnification (m) = Height of Image (hi) / Height of Object (ho).
• m > 1 for a magnified image, m < 1 for a reduced image, and m = 1 for the same-sized image.

Applications:

• Concave mirrors are used in makeup mirrors, telescopes, and satellite dishes.
• Convex mirrors are used in car side-view mirrors and security mirrors.

Safety Tips:

• Do not direct sunlight onto objects using concave mirrors as they can cause fires due to the concentration of sunlight.
• Use safety precautions while handling mirrors to avoid breakage and sharp edges.

Let’s practice!