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CLASS 12 • PHYSICS
Ray Optics
1. Spherical Mirrors
Mirror Formula
$\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$
Concave f is (-), Convex f is (+)
Magnification
$m = \frac{h_i}{h_o} = -\frac{v}{u}$
Relation R and f
$R = 2f$
2. Refraction Basics
Snell's Law
$\mu_1 \sin i = \mu_2 \sin r$
Apparent Depth
$d_{app} = \frac{d_{real}}{\mu}$
Shift = $d(1 - 1/\mu)$
Critical Angle (TIR)
$\sin i_c = \frac{1}{\mu}$
Ray from Denser to Rarer
3. Lenses
Lens Maker's Formula
$\frac{1}{f} = (\mu - 1)(\frac{1}{R_1} - \frac{1}{R_2})$
Thin Lens Formula
$\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$
Note the MINUS sign!
Power of Lens
$P = \frac{1}{f(in\ meters)}$
Unit: Diopter (D)
Combination of Lenses
$P = P_1 + P_2 + P_3...$
Sign convention applies to P
4. The Prism
Deviation ($\delta$)
$\delta = i + e - A$
Refractive Index
$\mu = \frac{\sin((A+\delta_m)/2)}{\sin(A/2)}$
$\delta_m$ = Min Deviation (where $i=e$)
Dispersion (Thin Prism)
$\delta = (\mu - 1)A$
5. Compound Microscope
Magnification (Near Point D)
$M = \frac{L}{f_o} (1 + \frac{D}{f_e})$
Max Magnification
Magnification (Infinity)
$M = \frac{L}{f_o} (\frac{D}{f_e})$
Normal Adjustment (Relaxed Eye)
Length of Tube
$L = v_o + u_e$
6. Telescope
Magnification (Infinity)
$M = \frac{f_o}{f_e}$
Most common formula used
Magnification (Near Point)
$M = \frac{f_o}{f_e} (1 + \frac{f_e}{D})$
Tube Length
$L = f_o + f_e$
7. Common Exam Traps
- ⚠️ Mirror vs Lens: Mirror formula has PLUS ($+$), Lens formula has MINUS ($-$). Don't mix them up!
- ⚠️ Sign Convention: Light travels Left to Right. Distance measured in direction of light is POSITIVE. Against it is NEGATIVE. Up is (+), Down is (-).
- ⚠️ Compound Microscope: $f_o$ is small, $f_e$ is moderate. In Telescope: $f_o$ is very large, $f_e$ is small.
8. Golden Theory Rules
- Scattering: Blue light scatters most ($\text{Intensity} \propto 1/\lambda^4$). That's why sky is blue.
- TIR Conditions: 1. Light must travel Denser to Rarer. 2. Angle of incidence $i > i_c$.
- Rainbow: Primary Rainbow involves 2 refractions + 1 internal reflection. Secondary involves 2 refractions + 2 internal reflections.
