Class 12 Physics - Quick Revision Notes

Chapter: Ray Optics and Optical Instruments (MP Board)

Laws of Reflection (परावर्तन के नियम):
1. The angle of incidence ($i$) is equal to the angle of reflection ($r$). $\rightarrow \angle i = \angle r$
2. The incident ray, the normal to the mirror at the point of incidence, and the reflected ray all lie in the same plane.
Mirror Formula (दर्पण सूत्र): $$\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$$
- Where:
  - $f$ = Focal length (फोकस दूरी)
  - $v$ = Image distance (प्रतिबिम्ब की दूरी)
  - $u$ = Object distance (वस्तु की दूरी)
Linear Magnification (रैखिक आवर्धन - $m$): $$m = \frac{h_2}{h_1} = -\frac{v}{u}$$
- Where $h_1$ is the height of the object and $h_2$ is the height of the image.
- Note: Relation between focal length and radius of curvature ($R$): $f = \frac{R}{2}$

Snell's Law (स्नेल का नियम): $$\frac{\sin i}{\sin r} = \text{constant} = {^1}\mu_2 = \frac{n_2}{n_1}$$
- Where ${^1}\mu_2$ is the refractive index of medium 2 with respect to medium 1.
Absolute Refractive Index ($\mu$ or $n$): $$\mu = \frac{c}{v}$$
- Where $c$ = speed of light in vacuum, $v$ = speed of light in the medium.
Principle of Reversibility (उत्क्रमणीयता का सिद्धान्त): $${^1}\mu_2 \times {^2}\mu_1 = 1 \implies {^1}\mu_2 = \frac{1}{{^2}\mu_1}$$
Apparent Depth (आभासी गहराई): $$\mu = \frac{\text{Real Depth}}{\text{Apparent Depth}} = \frac{h}{h'}$$
- Shift in position ($x$): $x = h \left(1 - \frac{1}{\mu}\right)$

Conditions for TIR:
1. Light must travel from a denser medium to a rarer medium.
2. The angle of incidence must be greater than the critical angle ($i > i_c$).
Critical Angle ($i_c$): $$\sin i_c = \frac{1}{\mu}$$

Refraction at a Spherical Surface: $$\frac{\mu_2}{v} - \frac{\mu_1}{u} = \frac{\mu_2 - \mu_1}{R}$$
Lens Maker’s Formula (लेंस निर्माता सूत्र): $$\frac{1}{f} = (\mu - 1) \left(\frac{1}{R_1} - \frac{1}{R_2}\right)$$ (where $\mu$ is the refractive index of the lens material with respect to the surrounding medium).
Thin Lens Formula (पतला लेंस सूत्र): $$\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$$
Magnification for Lens (लेंस का आवर्धन): $$m = \frac{h_2}{h_1} = \frac{v}{u}$$
Power of a Lens (लेंस की क्षमता): $$P = \frac{1}{f \text{ (in meters)}} \quad \text{or} \quad P = \frac{100}{f \text{ (in cm)}}$$
- SI Unit: Dioptre (D)
Combination of Thin Lenses in Contact (संपर्क में रखे लेंसों का संयोजन): $$\frac{1}{F} = \frac{1}{f_1} + \frac{1}{f_2} + \dots$$ $$P = P_1 + P_2 + \dots$$ $$m = m_1 \times m_2 \times \dots$$

Angle of Deviation ($\delta$): $$\delta = (i + e) - A$$
- Where $A$ = Angle of the prism, $i$ = Angle of incidence, $e$ = Angle of emergence.
Refractive Index of Prism Material: $$\mu = \frac{\sin\left(\frac{A + \delta_m}{2}\right)}{\sin\left(\frac{A}{2}\right)}$$ (where $\delta_m$ is the angle of minimum deviation).

When final image is formed at the Least Distance of Distinct Vision ($D = 25\text{ cm}$): $$m = 1 + \frac{D}{f}$$
When final image is formed at Infinity ($v = \infty$): $$m = \frac{D}{f}$$

Magnifying Power ($m$): $$m = m_o \times m_e = -\frac{v_o}{u_o} \left(1 + \frac{D}{f_e}\right)$$
Length of the Microscope Tube ($L$): $$L = v_o + u_e$$ (Approximate: $L \approx v_o + f_e$)

Magnifying Power ($m$) when final image is at Infinity (Normal Adjustment): $$m = -\frac{f_o}{f_e}$$
Length of the Telescope Tube ($L$): $$L = f_o + f_e$$
Magnifying Power when final image is at Least Distance of Distinct Vision ($D$): $$m = -\frac{f_o}{f_e} \left(1 + \frac{f_e}{D}\right)$$ $$L = f_o + u_e$$

All the Best for your MP Board Class 12 Physics Examination!