Spherical Mirrors
Spherical Mirrors
A spherical mirror is part of a hollow sphere.
Types of Spherical Mirrors
-
Concave Mirror:
- Reflecting surface curves inward.
- Also called converging mirror.
-
Convex Mirror:
- Reflecting surface bulges outward.
- Also called diverging mirror.
Key Terminology
- Pole (P): Mid-point of mirror surface.
- Centre of Curvature ©: Center of sphere the mirror is part of.
- Radius of Curvature ®: Distance PC.
- Principal Axis: Line through P and C.
- Principal Focus (F): Point where reflected rays converge or appear to diverge.
- Focal Length (f): Distance PF.
- Aperture: Diameter of mirror’s reflecting surface.
Image Formation Rules
Concave Mirror
- Ray parallel to axis passes through F.
- Ray through F reflects parallel to axis.
- Ray through C reflects back on itself.
Convex Mirror
- Ray parallel to axis appears to diverge from F.
- Ray directed toward F reflects parallel to axis.
- Ray toward C reflects back on itself.
Image Formation by Spherical Mirrors
Concave Mirror Image Formation
| Object Position | Image Position | Size | Nature |
|---|---|---|---|
| Between Pole (P) & F | Behind mirror | Enlarged | Virtual, erect |
| At Focus (F) | At infinity | Highly enlarged | Real, inverted |
| Between C & F | Beyond C | Enlarged | Real, inverted |
| At Centre of Curvature © | At C | Same size | Real, inverted |
| Beyond C | Between F and C | Diminished | Real, inverted |
| At Infinity | At Focus (F) | Highly diminished | Real, inverted |
Convex Mirror Image Formation
| Object Position | Image Position | Size | Nature |
|---|---|---|---|
| Between Infinity & Pole | Between P and F behind mirror | Diminished | Virtual, erect |
| At Infinity | At focus behind mirror | Highly diminished | Virtual, erect |
Uses, Sign Convention, and Formulae
Uses of Concave Mirrors
- Shaving mirrors (enlarged face).
- Reflectors in headlights and torches.
- Solar furnaces.
- Medical instruments.
- Dental mirrors.
Uses of Convex Mirrors
- Rear-view mirrors in vehicles.
- Street lamps for wide area illumination.
Sign Convention
- Object always to the left: u negative.
- Distances right of mirror: positive.
- Heights above axis: positive.
- Heights below axis: negative.
If image is virtual and erect:
- v positive
- h2 positive
- m positive
If image is real and inverted:
- v negative
- h2 negative
- m negative
Formulae
-
Focal Length: [ f = \frac{R}{2} ]
-
Mirror Formula: [ \frac{1}{v} + \frac{1}{u} = \frac{1}{f} ]
-
Magnification: [ m = \frac{h_2}{h_1} = -\frac{v}{u} ]
Interpreting Magnification
- |m| > 1: Magnified
- |m| < 1: Diminished
- |m| = 1: Same size
- Positive m: Virtual, erect
- Negative m: Real, inverted
