Formula Sheet for OPTICS Part 2

1. Refraction at Spherical Surfaces:
- Snell's Law: n1sinθ1 = n2sinθ2
- Lensmaker's Formula: 1/f = (n - 1)(1/R1 - 1/R2)

2. Thin Lenses:
- Lens Formula: 1/f = 1/v - 1/u
- Magnification: m = -v/u = h'/h = -q/p
- Lens Power: P = 1/f (in diopters)
- Lens Maker's Formula: 1/f = (μ - 1)(1/R1 - 1/R2)

3. Combination of Thin Lenses:
- For lenses in contact: P = P1 + P2
- For lenses separated by a distance d: P = P1 + P2 - (d/μ)P1P2

4. Optical Instruments:
- Magnifying Power of a Telescope: MP = (-D/f1) × (D/f2) = (-L/f1) × (L/f2)
- Magnifying Power of a Microscope: MP = (-D'/f1) × (D'/f2) = (-L/f1) × (L/f2)
- Resolving Power of a Microscope: RP = 1.22 × (λ/2Nsinθ)
- Resolving Power of a Telescope: RP = 1.22 × (λ/2D)

5. Dispersion and Scattering of Light:
- Deviation angle for a Prism: δ = A(μ - 1)
- Angle of Minimum Deviation: δm = A - i + r
- Dispersive Power of a Prism: w = (μ - 1)/μ
- Rayleigh's Scattering Law: I ∝ 1/λ^4

6. Polarization:
- Malus' Law: I = I0cos^2θ
- Brewster's Law: tanθp = μ
- Law of Malus for Polarizers: I = I0cos^2θ1cos^2θ2...

7. Optical Activity:
- Specific Rotation: α = αobserved/(c × l)
- Percentage of Optical Activity: % Optical Activity = α × c × l × 100

8. Huygen's Principle:
- The wavefront at any instant is the envelope of the wavelets emitted by the sources at the preceding instant.

9. Interference:
- Path Difference: Δx = nλ (constructive), (2n+1)λ/2 (destructive)
- Fringe Width: β = λL/d
- Condition for Maxima in Thin Films: 2μt = (2n + 1)λ/2

10. Diffraction:
- Angular Width of Central Maximum: θ = λ/b
- Angular Width of Nth Maximum: θ = Nλ/b
- Condition for Maxima in Single Slit Diffraction: asinθ = nλ

This formula sheet provides a comprehensive overview of the key formulas in the OPTICS Part 2 section. It covers