Learning Objectives
- Understand reflection and refraction of light
- Study image formation by mirrors and lenses
- Learn about total internal reflection and its applications
- Understand prism dispersion and scattering of light
- Study optical instruments: microscope, telescope, eye
Key Concepts
Reflection at Spherical Mirrors
Mirror formula: 1/v + 1/u = 1/f
Magnification: m = -v/u = h'/h
f = R/2 (focal length = half of radius of curvature).
Sign convention: distances measured from pole; along incident ray positive; opposite negative.
Refraction
Snell's Law: n₁ sin i = n₂ sin r, or sin i/sin r = n₂/n₁ = v₁/v₂ = λ₁/λ₂
Refractive index: n = c/v (speed of light in vacuum / speed in medium).
Light bends toward normal when entering a denser medium (n₂ > n₁).
Total Internal Reflection (TIR)
Occurs when light travels from denser to rarer medium and angle of incidence exceeds the critical angle.
Critical angle: sin C = n₂/n₁ (n₂ < n₁).
Applications: optical fibre, diamond brilliance, mirages, prism binoculars.
Refraction at Spherical Surfaces
n₁/u + n₂/v = (n₂ - n₁)/R
Thin Lens Formula
1/v - 1/u = 1/f
Lens Maker's formula: 1/f = (n - 1)(1/R₁ - 1/R₂)
Magnification: m = v/u = h'/h
Power: P = 1/f (in dioptres, D, when f is in metres).
Combination: P = P₁ + P₂ or 1/f = 1/f₁ + 1/f₂ (thin lenses in contact).
Prism
Deviation: δ = (i + e) - A, where A is the prism angle.
At minimum deviation: i = e, r₁ = r₂ = A/2, n = sin[(A + δ_m)/2] / sin(A/2).
Dispersion: Splitting of white light into constituent colours. Violet deviates most, red least.
Angular dispersion: δ_V - δ_R. Dispersive power: ω = (δ_V - δ_R)/δ_Y = (n_V - n_R)/(n_Y - 1).
Optical Instruments
Simple microscope: m = 1 + D/f (D = 25 cm = least distance of distinct vision).
Compound microscope: m = m_o × m_e = (L/f_o)(1 + D/f_e), where L = tube length.
Astronomical telescope (normal adjustment): m = -f_o/f_e, L = f_o + f_e.
Reflecting telescope: Uses concave mirror as objective. Advantages: no chromatic aberration, can be made larger.
Scattering of Light
Rayleigh scattering: Intensity ∝ 1/λ⁴. Blue light scattered more than red. Explains blue sky, red sunset.
Summary
Ray optics uses rectilinear propagation to explain reflection, refraction, and image formation. Mirror and lens formulas relate object distance, image distance, and focal length. Total internal reflection occurs above the critical angle. Prisms disperse white light. Optical instruments use combinations of lenses and mirrors to magnify images. Rayleigh scattering explains colour phenomena in the sky.
Important Terms
- Focal Length: Distance from optical centre to focus
- Refractive Index: Ratio of speed of light in vacuum to speed in medium
- Critical Angle: Angle of incidence for which angle of refraction is 90°
- Dispersion: Splitting of light into constituent colours
- Power of Lens: P = 1/f (dioptre)
- Magnifying Power: Ratio of angle subtended by image to angle subtended by object
Quick Revision
- Mirror: 1/v + 1/u = 1/f; Lens: 1/v - 1/u = 1/f
- Snell's law: n₁ sin i = n₂ sin r; TIR: sin C = n₂/n₁
- Lens maker: 1/f = (n-1)(1/R₁ - 1/R₂); P = 1/f (dioptre)
- Prism: n = sin[(A+δ_m)/2]/sin(A/2)
- Telescope: m = f_o/f_e; Microscope: m = (L/f_o)(D/f_e)
- Rayleigh: I ∝ 1/λ⁴ (blue sky, red sunset)