Refraction of Light — Formula Sheet

Snell's Law: \frac{\sin i}{\sin r} = constant = {}_a n_g

{}_a n_g = \frac{Speed \in air}{Speed \in glass} = \frac{c}{v}, n=\frac{c}{v}

Wavelength relation: v_R = n \cdot \lambda_R;\ v_D = n \cdot \lambda_D;\ \lambda_D = \frac{v_D}{v_R}\lambda_R

Reversibility relation: {}_R n_D \times {}_D n_R = 1;\ {}_1 n_2 = \frac{1}{{}_2 n_1}

Lateral displacement: BY = t \sec r \sin(i-r)

n = A + \frac{B}{\lambda^{2}}

A = r_1 + r_2

\delta = i_1+i_2-A;\ i+e = A+\delta

\delta_{min}=2i-A;\ i=\frac{A+\delta_{min}}{2};\ r=A/2

\mu=\frac{\sin\left(\frac{A+\delta_{min}}{2}\right)}{\sin A/2}

\delta=(n-1)A

n=\frac{Real\ depth}{Apparent\ depth}

OO'=R\left(1-\frac{1}{n}\right)

d_{app}=\frac{d_1}{n_1}+\frac{d_2}{n_2}+\frac{d_3}{n_3}+\cdots