09Class 12 Physics

Ray Optics and Optical Instruments formulas

Mirror, lens, refraction and instrument formulas for Ray Optics. Most marks are lost to signs, so fix your convention before calculating.

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Mirrors

Snell's law: $\displaystyle n_1\sin i = n_2\sin r$
Apparent depth: $\displaystyle \text{apparent depth} = \frac{\text{real depth}}{n}$
Critical angle: $\displaystyle \sin C = \frac{1}{n}$
For light going from the denser medium into air.
Refraction at a spherical surface: $\displaystyle \frac{n_2}{v} - \frac{n_1}{u} = \frac{n_2 - n_1}{R}$

Lens equation: $\displaystyle \frac{1}{v} - \frac{1}{u} = \frac{1}{f}$
Lens maker's formula: $\displaystyle \frac{1}{f} = (n - 1)\left(\frac{1}{R_1} - \frac{1}{R_2}\right)$
Magnification: $\displaystyle m = \frac{v}{u}$
Power: $\displaystyle P = \frac{1}{f}$
f in metres gives P in dioptres.
Lenses in contact: $\displaystyle \frac{1}{f} = \frac{1}{f_1} + \frac{1}{f_2}, \quad P = P_1 + P_2$

Prism angles: $\displaystyle A = r_1 + r_2, \quad \delta = i + e - A$
Refractive index of a prism: $\displaystyle n = \frac{\sin\frac{A + \delta_m}{2}}{\sin\frac{A}{2}}$
Thin prism: $\displaystyle \delta = (n - 1)A$
Simple microscope: $\displaystyle m = 1 + \frac{D}{f}$
Image at the near point D.
Compound microscope: $\displaystyle m = \frac{L}{f_o}\cdot\frac{D}{f_e}$
Telescope: $\displaystyle m = \frac{f_o}{f_e}$
Normal adjustment. Tube length is f_o + f_e.

Using the mirror equation for a lens. The sign in front of 1/u differs, and so does magnification.
Using f in centimetres for lens power. Convert to metres first.
Assuming total internal reflection can happen going from rarer to denser. It only works from denser to rarer.

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