# List of formulas related to gemetric optics

## Laws Of Reflection

SI: incident ray, IR: reflected ray, i: angle of incidence, i’: angle of reflection

$$i = i'$$

### Refractive Index

n: refractive index of the medium, v: speed of light in a medium, c: speed of light in vacuum (m/s)

$$n = \frac{c}{v}$$

### Law Of Refraction

n1: refractive index of the medium 1, n2: refractive index of medium 2, i: angle of incidence, r: angle of refraction, n21: absolute index of refraction

$$\frac{sin i}{sin r} = n_{21} = \frac{n_2}{n_1}$$ $$\frac{n_1}{n_2} = \frac{v_1}{v_2}$$ $$v_1 = c =3.10^8 m/s$$ $$n_1 = 1$$ $$=> n_2 = \frac{c}{v_2}$$

### Total Reflection Phenomenon

There is no refracted ray if

$$n_1 > n_2$$ $$i > i_c, sin i_c = \frac{n_2}{n_1}$$

### Prism

A: apex angle, D: deviation angle, i1: angle of incidence, i2: angle of emergent ray

$$sin i _1 = nsin r _1$$ $$sin i_2 = nsin r_2$$ $$A = r_1 + r_2$$ $$D = i_1 + i_2 - A$$ $$\text{Condition to have refractive ray}$$ $$A \leq 2i_{gh}$$ $$i \geq i_o$$ $$sin i_o = nsin(A - \tau)$$ $$\text{When angle of incidence is minimum}$$ $$d - > D_{min} : i_1 = i_2 = i$$ $$r_1 = r_2 = \frac{A}{2}$$ $$sin \frac{D_{min} + A}{2} = nsin \frac{A}{2}$$ $$=> D_{min} = 2i - A$$

### Thin Lens

f: focal length (converging len f>0; diverging len f<0), d: object distance from lens center, d’: image distance from lens center

$$\frac{1}{f} = \frac{1}{d} + \frac{1}{d'} => f = \frac{d.d'}{d + d'}$$ $$d = \frac{d'.f}{d' - f'} ; {d'} = \frac{df}{d - f}$$

### Magnification Factor

hI ; image height, ho: object height

$$k = \frac{h_1}{h_o} = - \frac{d'}{d} = \frac{-f}{d - f} = \frac{d' - f}{f}$$

#### Power Of The Lens

n: refractive index of the lens material, R1: radius of curvature of the lens surface closest to the light source, R2: radius of curvature of the lens surface farthest from the light source

$$D = \frac{1}{f} = (n - 1) (\frac{1}{R_1} + \frac{1}{R_2})$$