Optics is the branch of physics that tells how the light behaves, its properties and its interactions. There are many formulas in optics. Some of them are,

Refractive index,
n = $\frac{Speed \ of \ light \ in \ vacuum}{Speed \ of \ light \ in \ a \ medium}$ = $\frac{c}{v}$

Snell's law of refraction: If n1 and n2 are the refractive indexes of medium 1 and medium 2 and $\theta_1$ is the angle of the incident ray and $\theta_2 is the angle of refracted ray.

The snell's law is given by,
n1 sin $\theta_1$ = n2 sin $\theta_2$.

The critical angle is given by,
sin $\theta_c$ = $\frac{n_1}{n_2}$.

Mirror formula,
$\frac{1}{u}$  + $\frac{1}{v}$ = $\frac{1}{f}$.

Where,
u is image distance,
v is the object distance,
f is the focal length.

Magnification,
m = $\frac{v}{u}$ = $\frac{v-f}{f}$ = $\frac{f}{u-f}$,
or
m = $\frac{I}{O}$.

Thin lens formula,
$\frac{1}{f}$ = $\frac{1}{v} - \frac{1}{u}$
Where, u is image distance, v is object distance.


The power of lens is given by,
P = $\frac{1}{Focal\ length}$.

The equivalent focal length of two lens in contact is given by,
$\frac{1}{F}$ = $\frac{1}{f_1} + \frac{1}{f_2}$.

Where,
f1 is the focal length of the lens 1,
f2 is the focal length of the lens 2,
F is equivalent focal length..

Below are given some examples on optics, you can go through:

Question 1: The light rays travels from air to water at an incidence angle of 420. Calculate its reflection angle.
Solution:
Given: R.I in air n1 = 1, R.I in water n2 = 1.33, angle of incidence $\theta_1$ = 420
The snell's law formula is given by : n1 sin $\theta_1$ = n2 sin $\theta_2$

The angle of reflection $\theta_2$ is given by,

Sin $\theta_2$ = $\frac{n_1 sin \theta_1}{n_2}$

Sin $\theta_2$ = $\frac{1 \times sin 42^0}{1.33}$

Sin $\theta_2$ = 0.503

Therefore, reflection angle, $\theta_2$ is 30.2$^{\circ}$.

Question 2: The light has a speed in glass as 2.32 $\times$ 108 m/s.Calculate the refractive index of glass.
Solution:
Given: Speed of light in glass v = 2.32 $\times$ 108 m/s, Speed of light in vacuum = 3 $\times$ 108 m/s

The refractive index n is given by,

Refractive index, n = $\frac{Speed \ of \ light \ in \ vacuum}{Speed \ of \ light \ in \ a \ medium}$

n = $\frac{c}{v}$

n = $\frac{3 \times 10^8 m/s}{2.32 \times 10^8 m/s}$

 n = 1.29.

Therefore, refractive index of glass is 1.29.