Dispersion of Light Explained
Dispersion is the phenomenon where white light separates into its constituent colors when passing through a prism or other medium. Different colors (wavele
TL;DR: Dispersion is the phenomenon where white light separates into its constituent colors when passing through a prism or other medium. Different colors (w…
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Dispersion of Light: Dispersion is the phenomenon where white light separates into its constituent colors when passing through a prism or other medium. Different colors (wavele
Dispersion of Light Explained Simply
Dispersion is the phenomenon where white light separates into its constituent colors when passing through a prism or other medium. Different colors (wavele This is a key Physics concept for Class 10.
🎬 Watch the animated, step-by-step Dispersion of Light diagram →
What is Dispersion?
Dispersion is the splitting of white light into its component colors (spectrum) due to different refractive indices for different wavelengths. White light contains all visible wavelengths from violet (400 nm) to red (700 nm). When light passes through a prism, violet light bends more than red light because it travels slower in glass. This differential bending causes spatial separation of colors.
Refractive Index and Wavelength
The refractive index of a medium depends on the wavelength of light. This property is called dispersion. For most transparent media like glass, shorter wavelengths (violet, blue) have higher refractive indices than longer wavelengths (red, orange). This is normal dispersion. The relationship can be expressed as n = a + b/λ^2, where n is refractive index and λ is wavelength.
The Visible Spectrum
When white light is dispersed, it produces the visible spectrum in order: Violet (380-450 nm), Indigo (450-495 nm), Blue (495-570 nm), Green (570-590 nm), Yellow (590-620 nm), Orange (620-750 nm), Red (750-780 nm). A common mnemonic is VIBGYOR. Red light has the longest wavelength and bends least, while violet light has the shortest wavelength and bends most in a prism.
Dispersion through a Prism
When a narrow beam of white light passes through a prism, it refracts at the first surface entering the prism, then at the second surface exiting. Due to different refractive indices for different colors, each color exits at a different angle. The angle between the incident ray and the emergent ray is called the angle of deviation. Red light has minimum deviation; violet light has maximum deviation.
Causation of Rainbows
A rainbow is a natural example of dispersion caused by water droplets in the atmosphere. Sunlight enters a water droplet, refracts and disperses into colors, reflects internally once (or twice for secondary rainbow), and refracts again while exiting. Each color exits at a different angle (deviation of about 42° for primary rainbow), creating the arc of colors. The water droplets must be behind the observer with the sun in front.
Angular Dispersion
Angular dispersion is the difference in deviation angles between two colors. It is defined as the angle between the emergent rays of the two colors. For a prism, angular dispersion depends on the angle of the prism (A), the refractive indices of the two colors (n1 and n2), and the angle of incidence. Greater angular dispersion indicates better color separation.
Worked Examples
Example 1. A prism has an angle of 60° and refractive indices for red and violet light are 1.51 and 1.53 respectively. If the angle of incidence is 45°, compare the deviations for red and violet light qualitatively.
Solution: Given: A = 60°, n_red = 1.51, n_violet = 1.53, i = 45°
The angle of deviation depends on refractive index by: r1 + r2 = A + δ (approximately for small angles)
Since n_violet > n_red, violet light bends more at both surfaces.
Thus r1_violet < r1_red and r2_violet < r2_red
Therefore δ_violet > δ_red
Violet light has greater deviation than red light, indicating violet bends more as expected.
Example 2. In a spectrum produced by a prism, the wavelength of red light is 700 nm and violet light is 400 nm. If the refractive index of the prism material varies as n = 1.5 + 50/λ^2 (where λ is in nm), find the refractive indices for both colors.
Solution: For red light: λ = 700 nm
n_red = 1.5 + 50/(700)^2 = 1.5 + 50/490000 = 1.5 + 0.0001 = 1.5001
For violet light: λ = 400 nm
n_violet = 1.5 + 50/(400)^2 = 1.5 + 50/160000 = 1.5 + 0.0003 = 1.5003
Since n_violet > n_red, violet light travels slower and bends more in the prism.
Example 3. A ray of white light is incident at 50° on a prism of angle 60°. If the refractive index for red and violet light are 1.5 and 1.6 respectively, which color deviates more?
Solution: Using the prism formula for deviation: sin((A + δ)/2) = n sin(A/2) (approximately)
For red light with n = 1.5:
sin((60 + δ_red)/2) = 1.5 sin(30°) = 1.5 x 0.5 = 0.75
(60 + δ_red)/2 = 48.6°
δ_red = 37.2°
For violet light with n = 1.6:
sin((60 + δ_violet)/2) = 1.6 sin(30°) = 1.6 x 0.5 = 0.8
(60 + δ_violet)/2 = 53.1°
δ_violet = 46.2°
Violet light has greater deviation (46.2°) compared to red light (37.2°).
Where You See This in Real Life
- Rainbows seen in India after monsoon rains are natural examples of light dispersion by water droplets suspended in air.
- Prism instruments used in Indian laboratories and spectroscopy labs separate light into its spectral components for analysis and identification of elements.
- Chromatic aberration in cheap optical instruments used in Indian schools shows purple and red halos around objects because different colors focus at different points.
- The colorful patterns seen on soap bubbles and oil films (commonly seen in Indian streets) are due to interference and dispersion of light in thin films.
Common Mistakes Students Make
- Thinking dispersion only occurs in prisms. Dispersion occurs in any medium where different wavelengths have different speeds.
- Confusing dispersion with diffraction. Dispersion separates colors due to different refractive indices; diffraction is bending around obstacles.
- Assuming all colors refract by the same angle in a prism. In reality, the angle of refraction depends on wavelength and the material's refractive index.
- Not recognizing that the order of colors in a spectrum is always VIBGYOR from violet (most bent) to red (least bent).
Frequently Asked Questions
Why is a secondary rainbow fainter than a primary rainbow?
In a secondary rainbow, light reflects twice inside water droplets instead of once. Each internal reflection causes some light loss, so less light reaches the observer. Also, the secondary rainbow lies above and outside the primary rainbow with inverted color order.
Why does a prism separate white light into colors but a plane mirror does not?
A prism causes refraction at non-parallel surfaces, bending different wavelengths by different amounts. A plane mirror just reflects all colors at the same angle, so no separation occurs.
Why can we see a rainbow only when the sun is behind us?
For dispersion by water droplets, the sun must be behind the observer so that light can enter the droplets, reflect and refract, and return to the observer's eyes at an angle of about 42° for the primary rainbow.