# Dispersion of light:

“It is the phenomena of splitting of a beam of white light into its constituent colours on passing through a prism.”

Spectrum:

“The band of seven colours obtained when a beam of white light is passed through a prism is called as spectrum of light.”

Band of colours:   

V                 I               B             G             Y            O                     R
Violet      Indigo        Blue      Green       Yellow    Orange         Red

Cause of dispersion:

Each colour has its own wavelength.

Since δ = (µ - 1) A                ∴ δ ∝ µ          Also µ ∝ 1/λ²

∴ δ ∝ µ ∝ 1/λ²

Or δ ∝ 1/λ²

∴ Angle of deviation is inversely proportional to wavelength.

∴ Red colour (having maximum wavelength) undergoes minimum deviation and violent colour (having minimum wavelength) undergoes maximum deviation. Rest of the colours are deviated with angle between that for red and violet.

# Angular dispersion (θ)

“Angular dispersion for white light is the difference in the angles of deviation suffered by the two extreme colour (red and violet) after passing through the prism”

Angular dispersion           θ = δ_v - δ_r

θ = (µ_v – 1)A – (µ_r – 1)A

θ = (µ_v - µ_r)A

  δ = (µ - 1)A                       

  δ_v = (µ_v - 1)A

δ_r = (µ_r - 1)A

∴ Angular dispersion depends on

(i) Angle of prism

(ii) Refractive index of material of prism

# Dispersive power of a prism (ω):

“Dispersive power of a prism is defined as the ratio of angular dispersion to the mean deviation produced by the prism”

∴ Dispersive power = Angular dispersion/Mean deviation (deviation for mean (yellow colour))

ω = (δ_v - δ_r/δ_y) = (µ_v - µ_r)A/µ_y – 1)A

ω = (µ_v - µ_r)/µ_y – 1

Note: (i) ω depends upon µ (ii) ω is independent of A.