Dispersion of Light — Revision Notes

⚡ 30-Second Revision

Dispersion: — Splitting of white light into constituent colors (VIBGYOR).
Cause: — Refractive index ($n$) varies with wavelength ($lambda$). $n_{\text{violet}} > n_{\text{red}}$.
Deviation: — $\delta = (n-1)A$. Violet deviates most, Red deviates least ($\delta_V > \delta_R$).
Angular Dispersion ($\theta$): — Angular separation between two colors (e.g., V & R).

$\theta = \delta_V - \delta_R = (n_V - n_R)A$.

Dispersive Power ($\omega$): — Material property, dimensionless.

$\omega = \frac{\delta_V - \delta_R}{\delta_Y} = \frac{n_V - n_R}{n_Y - 1}$.

Rainbows: — Natural example of dispersion (water droplets act as prisms).
Chromatic Aberration: — Lens defect due to dispersion.

2-Minute Revision

Dispersion of light is the phenomenon where white light, a mixture of colors, separates into its individual components (VIBGYOR) upon passing through a transparent medium like a prism. This occurs because the medium's refractive index ($n$) is not constant for all colors; it's higher for shorter wavelengths (violet) and lower for longer wavelengths (red). Consequently, violet light bends (deviates) the most, and red light bends the least, leading to their angular separation.

Key quantities to remember are angular dispersion ($\theta$), which is the actual angular spread between two colors (typically violet and red), calculated as $\theta = (n_V - n_R)A$, where $A$ is the prism angle.

This value depends on both the material and the prism's geometry. The other crucial concept is dispersive power ($omega$), a dimensionless property of the material itself, defined as the ratio of angular dispersion to the mean deviation (deviation of yellow light): $\omega = \frac{n_V - n_R}{n_Y - 1}$.

Dispersive power is independent of the prism angle. Remember that dispersion requires polychromatic light and a medium with wavelength-dependent refractive index. Don't confuse it with scattering, which explains the blue sky.

5-Minute Revision

Dispersion of light is a fundamental optical phenomenon where a beam of white light, composed of various colors (wavelengths), splits into its constituent spectral components (VIBGYOR) when it traverses a transparent medium.

The underlying principle is that the speed of light in a medium, and thus its refractive index ($n$), varies with its wavelength ($lambda$). For most materials, the refractive index is higher for shorter wavelengths (like violet light) and lower for longer wavelengths (like red light).

This means $n_{\text{violet}} > n_{\text{red}}$.

When white light enters a prism, each color refracts by a different amount. The angle of deviation ($delta$) for a small-angled prism is given by $\delta = (n-1)A$. Since $n_V > n_R$, it follows that $\delta_V > \delta_R$. Therefore, violet light deviates the most, and red light deviates the least, causing the colors to separate and form a spectrum.

Two important quantitative measures related to dispersion are:

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Angular Dispersion ($\theta$): — This is the angular separation between any two colors in the spectrum, usually violet and red. It is calculated as the difference in their deviations:

$$\theta = \delta_V - \delta_R = (n_V - 1)A - (n_R - 1)A = (n_V - n_R)A$$

Angular dispersion depends on both the material (through $n_V - n_R$) and the geometry of the prism (through $A$).

1
Dispersive Power ($\omega$): — This is a dimensionless property of the material itself, quantifying its ability to disperse light relative to its mean deviation. It is defined as:

$$\omega = \frac{\text{Angular Dispersion}}{\text{Mean Deviation}} = \frac{\delta_V - \delta_R}{\delta_Y} = \frac{(n_V - n_R)A}{(n_Y - 1)A} = \frac{n_V - n_R}{n_Y - 1}$$

Here, $n_Y$ is the refractive index for yellow light (or mean light). Crucially, dispersive power is independent of the prism angle $A$. A higher $\omega$ indicates a material that spreads the spectrum more for a given overall bending.

Worked Example: A prism of angle $6^circ$ has refractive indices $n_V = 1.54$ and $n_R = 1.51$. The refractive index for yellow light is $n_Y = 1.52$.

Angular Dispersion: — $\theta = (n_V - n_R)A = (1.54 - 1.51) \times 6^circ = 0.03 \times 6^circ = 0.18^circ$.
Dispersive Power: — $\omega = \frac{n_V - n_R}{n_Y - 1} = \frac{1.54 - 1.51}{1.52 - 1} = \frac{0.03}{0.52} \approx 0.0577$.

Real-world applications include rainbows (water droplets acting as prisms) and chromatic aberration in lenses (different colors focusing at different points due to dispersion). It's vital to distinguish dispersion from scattering (e.g., blue sky), as they are distinct phenomena.

Prelims Revision Notes

Dispersion of Light: NEET Quick Facts

1. Definition: The phenomenon of splitting of white light into its constituent colors (VIBGYOR) when passing through a transparent medium.

2. Cause:

* White light is polychromatic (mixture of wavelengths). * Refractive index ($n$) of the medium varies with wavelength ($lambda$). This is called chromatic dispersion. * Generally, for visible light, $n$ decreases as $lambda$ increases (Cauchy's formula: $n = A + B/\lambda^2$). * Therefore, $n_{\text{violet}} > n_{\text{indigo}} > \dots > n_{\text{red}}$.

3. Deviation by a Prism:

* Angle of deviation $\delta = (n-1)A$ (for small prism angle $A$). * Since $n_V > n_R$, it implies $\delta_V > \delta_R$. * Order of Deviation: Violet (most) > Indigo > Blue > Green > Yellow > Orange > Red (least).

4. Angular Dispersion ($\theta$):

* Definition: Angular separation between two extreme colors (usually violet and red) in the spectrum. * Formula: $\theta = \delta_V - \delta_R = (n_V - n_R)A$. * Dependence: Depends on both the material (difference in refractive indices) and the prism angle $A$. * Units: Radians or degrees.

5. Dispersive Power ($\omega$):

* Definition: A dimensionless property of the material, representing its ability to disperse light relative to its mean deviation. * Formula: $\omega = \frac{\delta_V - \delta_R}{\delta_Y} = \frac{(n_V - n_R)A}{(n_Y - 1)A} = \frac{n_V - n_R}{n_Y - 1}$. * $n_Y$: Refractive index for yellow (mean) light, often approximated as $n_Y \approx (n_V + n_R)/2$. * Dependence: Depends ONLY on the material properties ($n_V, n_R, n_Y$), independent of prism angle $A$. * Units: Dimensionless.

6. Conditions for Dispersion:

* Incident light must be polychromatic (e.g., white light). * The transparent medium must have a refractive index that varies with wavelength.

7. Applications/Examples:

* Rainbows: Sunlight dispersed by water droplets (acting as tiny prisms). * Chromatic Aberration: Lens defect where different colors focus at different points due to dispersion. * Spectrometers: Instruments using prisms to analyze light spectra.

8. Common Misconceptions to Avoid:

* Dispersion vs. Scattering: Dispersion separates colors due to differential bending; scattering redirects light (e.g., blue sky is scattering, not dispersion). * Monochromatic Light: A prism only deviates monochromatic light; it does not disperse it. * Prism 'creates' colors: Prism only separates pre-existing colors in white light. * Dispersive power vs. Angular dispersion: Remember their distinct dependencies on prism angle.

Vyyuha Quick Recall

To remember the order of colors in the spectrum from least deviated (longest wavelength) to most deviated (shortest wavelength): Rich Old Young Girls Buy In Van. (Red, Orange, Yellow, Green, Blue, Indigo, Violet).