Spherical Mirrors

🔍 Concave Mirror

Curves inward like a cave. The reflecting surface is on the concave (inward) side. Converges light rays to a focal point. Used in telescopes, headlights, and shaving mirrors.

🔮 Convex Mirror

Curves outward like a dome. The reflecting surface is on the convex (outward) side. Diverges light rays. Used in car side mirrors, security mirrors, and street corners.

📚 Worked Examples

Problem 1: A concave mirror has a radius of curvature of 30 cm. Find its focal length.

Step 1: Given: Radius of curvature (R) = 30 cm

Step 2: Using the relationship: R = 2f

Step 3: Therefore: f = R/2 = 30/2 = 15 cm

Answer: The focal length is 15 cm

Problem 2: A convex mirror has a focal length of -20 cm. What is its radius of curvature?

Step 1: Given: Focal length (f) = -20 cm (negative for convex mirror)

Step 2: Using the relationship: R = 2f

Step 3: Therefore: R = 2 × (-20) = -40 cm

Answer: The radius of curvature is -40 cm

🎯 Test Your Knowledge

1. What type of mirror is used in car side mirrors?

Concave mirror

Convex mirror

Plane mirror

Parabolic mirror

2. If the radius of curvature of a concave mirror is 24 cm, what is its focal length?

24 cm

12 cm

48 cm

6 cm

3. Which point represents the center of the sphere from which a spherical mirror is cut?

Pole (P)

Centre of Curvature (C)

Focus (F)

Principal axis

4. A concave mirror can be used to burn paper by focusing sunlight. At which point should the paper be placed?

At the pole

At the centre of curvature

At the principal focus

Between pole and focus

🎓 Key Takeaways

Mirror Types

Concave mirrors converge light (cave inward) with the reflecting surface on the concave side, while convex mirrors diverge light (bulge outward) with the reflecting surface on the convex side.

Important Terms

Pole (P) - center of mirror surface, Centre of Curvature (C) - center of sphere, Principal Axis - line through P and C.

Focal Length Formula

For all spherical mirrors: R = 2f, where R is radius of curvature and f is focal length.

Applications

Concave: telescopes, headlights, solar furnaces. Convex: security mirrors, vehicle mirrors for wider view.