1. Reflection by Spherical Mirrors
- Concave Mirror: Converging mirror. Forms mostly real, inverted images (except when the object is placed exceptionally close between $P$ and $F$, where it forms an erect, magnified virtual image). Used in solar furnaces and dentist headlamps.
- Convex Mirror: Diverging mirror. Always forms a diminished, virtual, and erect image regardless of position. Used as rear-view vehicle mirrors due to a wider field of view.
2. The Mirror Formula & Magnification
Mirror Formula: $$\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$$
Magnification ($m$): $$m = \frac{h'}{h} = -\frac{v}{u}$$
(Where $u$ = object distance, $v$ = image distance, $f$ = focal length, $h'$ = image height, $h$ = object height)
3. Refraction & Laws (Snell's Law)
The bending of light rays when transitioning obliquely from one transparent optical medium to another due to changes in light speed.
- Snell's Law: The ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant value for light of a given color and pair of media.
$$\frac{\sin i}{\sin r} = \text{constant} = n_{21} \quad \text{(Refractive Index of medium 2 w.r.t 1)}$$
4. Lens Formula & Power
Lens Formula: $$\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$$
Magnification ($m$): $$m = \frac{h'}{h} = \frac{v}{u}$$
Power of a Lens ($P$): $$P = \frac{1}{f \text{ (in meters)}}$$ $\quad$ Unit: **Dioptre (D)**
CBSE Numerical Sign Convention Trick
Always Remember: Object distance ($u$) is **always negative** ($-$) in all mirror and lens calculations. The focal length ($f$) of a concave mirror/lens is **always negative** ($-$), whereas the focal length of a convex mirror/lens is **always positive** ($+$). Keeping this straight prevents silly calculation mistakes!