Spherical Mirrors and Laws of Reflection
Laws of Reflection:
- The angle of incidence equals the angle of reflection: $\angle i = \angle r$.
- The incident ray, normal to the mirror at the point of incidence, and the reflected ray all lie in the identical geometric plane.
Mirror Formula & Sign Convention (Cartesian):
- Object distance ($u$) is always negative.
- Focal length ($f$): Negative for Concave mirror, Positive for Convex mirror.
$$\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$$
Magnification ($m$):
$$m = \frac{h_i}{h_o} = -\frac{v}{u}$$
- If $m < 0$, image is real and inverted.
- If $m > 0$, image is virtual and erect.
- If $|m| > 1$, image is magnified; if $|m| < 1$, image is diminished.
Refraction and Snell's Law
When a light ray travels obliquely from one transparent medium into another, it bends at the interface due to a change in propagation speed:
- Travelling from rarer to denser medium: Bends towards the normal.
- Travelling from denser to rarer medium: Bends away from the normal.
Snell's Law of Refraction:
For a given pair of media and color of light:
$$\frac{\sin i}{\sin r} = \text{constant} = n_{21} = \frac{v_1}{v_2}$$
Where $n_{21}$ is the refractive index of medium 2 with respect to medium 1.
Absolute Refractive Index ($n$): $n = \frac{c}{v}$ where $c = 3 \times 10^8\text{ m/s}$.
Spherical Lenses: Formulas and Power
Lens Formula:
$$\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$$
Magnification for Lens:
$$m = \frac{h_i}{h_o} = +\frac{v}{u}$$
Power of a Lens ($P$):
The degree of convergence or divergence of light rays achieved by a lens:
$$P = \frac{1}{f\text{ (in meters)}}$$
- SI Unit: Dioptre (D) ($1\text{ D} = 1\text{ m}^{-1}$).
- Convex Lens: $f > 0 \implies P > 0$ (Positive dioptres).
- Concave Lens: $f < 0 \implies P < 0$ (Negative dioptres).
