Class 12 Physics Ray Optics Formulas

•  1st Law of Reflection

$\theta_i = \theta_r$

• Relation Between Focal Length and Curvature Radius 

$f = \frac{R}{2}$

• Mirror Formula for spherical mirrors:

$\frac{1}{f} = \frac{1}{u} + \frac{1}{v}$

• Magnification Through Mirror:

$m = \frac{\text{height of image}}{\text{height of object}} = \frac{v}{u}$

• Speed of Image (Object Moving in Front of Mirror with speed u')

For Spherical Mirror: $v' = -\frac{v^2}{u^2} \cdot u'$

For a plane mirror: $v' = 2u'$

• Number of images for n-Plane Mirrors at Angle θ

Number of images formed: $N = \frac{360^\circ}{\theta} - 1$, If $\frac{360^\circ}{\theta}$ is an integer.

Number of images formed: $N = \text{Integer part of } \frac{360^\circ}{\theta}$, ​If $\frac{360^\circ}{\theta}$ is not an integer.

Snell’s Law in Mathematical Form

$$n_1\sin {\theta }_1=n_2\sin {\theta }_2$$

Refractive Index (n)

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

• In terms of Wavelength

$$n=\frac{{\lambda }_0}{\lambda }$$

• Relative Refractive Index

$$n_{21} = \frac{n_2}{n_1}$$

• Critical Angle and Refractive Index

$$\sin C = \frac{n_2}{n_1} \quad \text{(for } n_1 > n_2\text{)}$$

Refraction through Lenses

• Lens Formula

$$\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$$

• Magnification Through Lenses

$$m = \frac{\text{height of image}}{\text{height of object}} = \frac{v}{u}$$

• Refraction Through a Spherical Surface

$$\frac{n_2}{v} - \frac{n_1}{u} = \frac{n_2 - n_1}{R}$$

• Power of a Lens

$$P = \frac{100}{f(\text{in cm})} = \frac{1}{f(\text{in m})} \quad \text{(in dioptres)}$$

• Combination of Lenses

$$P_{\text{total}} = P_1 + P_2 + P_3 + \dots$$

Angle of Deviation (δ)

$$\delta = (i_1 + i_2) - A$$

Minimum deviation (δm​):

$$i_1 = i_2, \quad r_1 = r_2 = \frac{A}{2}$$

Refractive Index of Prism

$$n=\frac{\sin \left(\frac{A+{\delta }_m}{2}\right)}{\sin \left(\frac{A}{2}\right)}$$

Angular Dispersion

$$\Delta \delta = \delta_v - \delta_r$$

Dispersive Power (ω)

$$\omega =\frac{n_v-n_r}{n_y-1}$$

Simple Microscope

• Magnifying Power

$$M = 1 + \frac{D}{f}$$

Compound Microscope

• Magnifying Power, it tell us how much bigger the image will be

$$M = \left( \frac{v}{u} \right) \times \left( 1 + \frac{D}{f_e} \right)$$

• If the object is very close to the focus of the objective lens

$$M \approx \frac{L}{f_o} \times \frac{D}{f_e}$$

• Angular Magnification, bigger angle means bigger image.

$$M = \frac{\text{angle subtended by image}}{\text{angle subtended by object at eye}}$$

• Resolving Power of Microscope, it tell us about clarity

$$\text{Resolving Power} = \frac{1}{d} = \frac{2 \mu \sin \theta}{\lambda}$$

Magnifying Power, tells us how much bigger the image will be.

$$M=\frac{f_o}{f_e}$$

• When the final image is at D which is 25 cm for humans.

$$M=\frac{f_o}{f_e}(1+\frac{f_e}{D})$$

Length of Telescope: adding both focal lengths

$$L=f_o+f_e$$

Resolving Power of Telescope

$$\text{Resolving Power} = \frac{1}{d} = \frac{1.22 \lambda}{D}$$