Optics, Lasers & Fibre Optics Notes

Last reviewed 16 Sept 2026 · 8 min read

Nature of light

Light shows wave behaviour (interference, diffraction, polarisation) and particle behaviour (photoelectric effect) — wave–particle duality.
Electromagnetic wave with speed $c = 3 \times 1 0^{8}$ m/s in vacuum; visible wavelengths about 400 nm (violet) to 700 nm (red).

Reflection and mirrors

Laws of reflection: angle of incidence = angle of reflection; incident ray, reflected ray and normal lie in one plane.
Plane mirror — virtual, erect, same size image, laterally inverted.
Spherical mirrors: focal length $f = R /2$ .

FormulaMirror formula (Cartesian sign convention)

\frac{1}{v} + \frac{1}{u} = \frac{1}{f}, m = - \frac{v}{u}

Refraction

FormulaSnell's law and refractive index

n_{1} sin θ_{1} = n_{2} sin θ_{2}, n = \frac{c}{v}

Light bends towards the normal entering a denser medium
Apparent depth $= \frac{real depth}{n}$ (objects under water appear raised)

Total internal reflection (TIR)

Occurs when light travels from denser to rarer medium at an angle greater than the critical angle:

sin θ_{c} = \frac{n _{2}}{n _{1}} = \frac{1}{n} (to air)

Glass (n ≈ 1.5) → θc ≈ 41.8°; water (n ≈ 1.33) → θc ≈ 48.8°; diamond (n ≈ 2.42) → ≈ 24.4° (sparkle).
Applications: optical fibres, prism binoculars/periscopes, reflecting prisms in surveying instruments (e.g. prism reflectors), mirages.

Atmospheric refraction

Stars twinkle; sun visible before actual sunrise; refraction correction in levelling and trigonometric levelling (see Surveying).

Lenses

FormulaLens formula (Cartesian sign convention)

\frac{1}{v} - \frac{1}{u} = \frac{1}{f}, m = \frac{v}{u}

Lens maker's formula: $\frac{1}{f} = (n - 1) (\frac{1}{R _{1}} - \frac{1}{R _{2}})$ Power $P = \frac{1}{f}$ (dioptre, D, with $f$ in metres); convex lenses positive, concave negative Lenses in contact: $P = P_{1} + P_{2}$

Convex (converging) lenses form real or virtual images; concave (diverging) lenses always form virtual, erect, diminished images.
Defects: spherical aberration, chromatic aberration (corrected by achromatic doublets).

Dispersion

Splitting of white light into colours due to variation of refractive index with wavelength (violet deviates most).
Prism deviation $δ = (n - 1) A$ for thin prisms; rainbow formation by dispersion and TIR in raindrops.

Optical instruments

Instrument	Principle	Magnification (normal adjustment)
Simple microscope	Convex lens as magnifier	$1 + D / f$ (image at D = 25 cm)
Compound microscope	Objective (short f) + eyepiece	$m = \frac{L}{f _{o}} \cdot \frac{D}{f _{e}}$ (approx.)
Astronomical telescope	Objective (long f) + eyepiece	$m = f_{o} / f_{e}$ ; tube length $f_{o} + f_{e}$
Surveying telescope (levels, theodolites, total stations)	Objective, focusing lens (internal focusing), diaphragm with cross hairs, eyepiece	Parallax removed by focusing eyepiece then objective

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Nature of light

Reflection and mirrors

Refraction

Total internal reflection (TIR)

Atmospheric refraction

Lenses

Dispersion

Optical instruments

This chapter is in the syllabus of