What Dispersion Is
Sunlight is polychromatic: it contains seven wavelengths corresponding to the colours violet, indigo, blue, green, yellow, orange and red (VIBGYOR). In free space, and to a very good approximation in air, every visible wavelength travels at the same speed, so they stay together and no colour separation occurs; such a medium is non-dispersive. Inside an optically denser medium the component wavelengths travel at different speeds and therefore have different refractive indices. This variation of refractive index with wavelength is what NIOS §21.1 calls dispersion.
The refractive index is $n = c/v$, the ratio of the speed of light in vacuum to its speed in the medium. Because the speed in glass depends on wavelength, $n$ is not a single number for white light — it is a function $n(\lambda)$. Shorter wavelengths travel slower in glass and so have a larger index. The phenomenon is therefore distinct from ordinary refraction: refraction bends a single ray, dispersion separates the colours within that ray.
Why a Prism, Not a Slab
Separating the colours is not by itself enough to observe dispersion: the colours must stay widely separated after leaving the medium. A rectangular glass slab fails this test. Its two refracting surfaces are parallel, so whatever small separation the first surface introduces is undone at the second; the emergent rays of all colours are parallel to each other and to the incident beam, lying too close together to be seen as a spectrum (NIOS Fig. 21.1).
A prism succeeds because its two refracting faces are inclined at the refracting angle $A$. White light entering face AB is bent, and the second face AC increases the separation between the colours rather than cancelling it. Newton used exactly this arrangement to show that white light is a mixture, with violet emerging closest to the base and red closest to the apex side, since violet is deviated most.
| Property | Glass slab | Prism |
|---|---|---|
| Refracting faces | Parallel | Inclined at angle $A$ |
| Emergent colours | Parallel, recombine | Diverge, stay separated |
| Net deviation of beam | Zero (lateral shift only) | Non-zero deviation $\delta$ |
| Spectrum visible? | No | Yes (VIBGYOR) |
Angle of Deviation and Wavelength
For a ray passing through a prism, the geometry of the principal section gives the deviation in terms of the angle of incidence $i$, the angle of emergence $e$, and the refracting angle $A$ (NIOS §21.1.2):
$$\delta = (i + e) - A, \qquad r_1 + r_2 = A.$$
As $i$ increases the deviation first falls to a minimum value $\delta_m$ and then rises again, so one deviation generally corresponds to two angles of incidence. At minimum deviation the ray passes symmetrically ($i = e$, $r_1 = r_2$), and the refractive index is
$$n = \frac{\sin\!\left(\dfrac{A + \delta_m}{2}\right)}{\sin\!\left(\dfrac{A}{2}\right)}.$$
For a thin (small-angle) prism, the sines may be replaced by their angles, and the deviation reduces to the relation NEET uses most often:
$$\delta = (n - 1)\,A.$$
Because $n$ depends on wavelength, $\delta$ depends on wavelength too. Violet has the largest index, so $n_v > n_r$, which forces $\delta_v > \delta_r$. Red light is the fastest colour in glass and is bent the least; violet is the slowest and is bent the most. This single inequality, $\delta_v > \delta_r$ following from $n_v > n_r$, is the heart of dispersion.
Violet bends most because of index, not "energy"
A common error is to reason that violet bends most "because it has the highest energy." The operative reason is purely optical: glass has the largest refractive index for the shortest wavelength, so $n_v > n_r$, and $\delta = (n-1)A$ then makes $\delta_v > \delta_r$. The ordering of deviations follows the ordering of refractive indices.
Remember: $n_v > n_r \Rightarrow \delta_v > \delta_r$. Violet most deviated, red least.
Angular Dispersion and Dispersive Power
The angular dispersion is the angle between the two extreme colours of the emerging beam, taken as violet and red:
$$\theta = \delta_v - \delta_r = (n_v - n_r)\,A.$$
Yellow light, lying near the middle of the spectrum, is taken as the mean colour, and its deviation $\delta_y = (n_y - 1)A$ represents the average deviation. The dispersive power $\omega$ is defined as the ratio of the angular dispersion to this mean deviation (NIOS §21.1.3):
$$\omega = \frac{\delta_v - \delta_r}{\delta_y} = \frac{(n_v - n_r)\,A}{(n_y - 1)\,A} = \frac{n_v - n_r}{n_y - 1}.$$
The prism angle $A$ cancels, leaving a quantity that depends only on the material. This is the single most tested fact in the subtopic.
Dispersive power vs angular dispersion
Angular dispersion $(\delta_v - \delta_r)$ is an angle — it grows when you increase the refracting angle $A$. Dispersive power $\omega$ is a pure number — dimensionless, with no units, and independent of $A$. Examiners frequently ask whether $\omega$ changes when the prism angle changes; it does not.
$\omega = (n_v - n_r)/(n_y - 1)$ is dimensionless and a property of the material alone.
The deviation formula $\delta = (n-1)A$ comes straight from prism geometry. Revisit the full derivation in Refraction Through a Prism.
Deviation and Dispersion Combinations
By combining two thin prisms of different materials with their refracting angles opposed, two useful conditions can be engineered. The mean deviation of a prism is $(n_y - 1)A$ and its angular dispersion is $(n_v - n_r)A$; pairing prisms lets one quantity be cancelled while the other survives.
| Combination | Condition | Result |
|---|---|---|
| Dispersion without deviation (direct-vision) | $(n_y-1)A = (n_y'-1)A'$ | Net deviation zero; dispersion remains |
| Deviation without dispersion (achromatic) | $(n_v-n_r)A = (n_v'-n_r')A'$ | Net dispersion zero; deviation remains |
A direct-vision prism is used in spectroscopes, where one wants the colours spread out but the beam to travel essentially straight. An achromatic combination underlies the correction of chromatic aberration in lenses, which NCERT notes as the cause of coloured fringes in thick lenses. The 2017 NEET question in the PYQ block below tests the dispersion-without-deviation condition directly.
Scattering: Blue Sky, Red Sun
Scattering is a separate optical effect from dispersion but is examined alongside it (NIOS §21.2). When sunlight meets particles smaller than its wavelength — chiefly air molecules — each particle absorbs and re-emits the light in all directions. The intensity of this scattered light follows Rayleigh's law:
$$I \propto \frac{1}{\lambda^4}.$$
The strong $\lambda^{-4}$ dependence means short wavelengths scatter far more than long ones. Blue is scattered roughly six times more than red, so light reaching the eye from all parts of the sky is rich in blue, and the sky looks blue. At sunrise and sunset the Sun's rays graze a long path through the atmosphere; the blue and violet are scattered out of the line of sight, and the transmitted light that reaches the observer is left rich in red, so the Sun appears red. Clouds, made of water droplets larger than the wavelength, scatter all colours equally and therefore look white.
Rayleigh scattering is 1/λ⁴, not 1/λ²
The intensity of Rayleigh-scattered light varies as the inverse fourth power of wavelength. Writing it as $1/\lambda^2$ is a frequent slip and changes the numerical ratio entirely. The same $\lambda^{-4}$ law explains both the blue sky and the red Sun — they are two sides of one phenomenon (light scattered away versus light transmitted through).
$I \propto 1/\lambda^4$: shortest wavelength scattered most intensely.
Worked Examples
The refracting angle of a prism is $30'$ and its refractive index is $1.6$. Find the deviation it produces. (NIOS Example 21.2)
For a thin prism, $\delta = (n-1)A$. Here $A = 30' = 0.5^\circ$, so $\delta = (1.6 - 1)\times 0.5^\circ = 0.6 \times 0.5^\circ = 0.3^\circ = 18'$.
A crown glass produces deviations of $2.84^\circ$, $3.28^\circ$ and $3.72^\circ$ for red, yellow and violet light. Find its dispersive power. (NIOS Terminal Exercise Q.6)
$\omega = \dfrac{\delta_v - \delta_r}{\delta_y} = \dfrac{3.72^\circ - 2.84^\circ}{3.28^\circ} = \dfrac{0.88}{3.28} \approx 0.27.$ Note that $\omega$ has no units; the degrees cancel.
For a prism of angle $A = 60^\circ$ the angle of minimum deviation is $A/2$. Find the refractive index. (NIOS Example 21.3)
With $\delta_m = 30^\circ$, $n = \dfrac{\sin[(A+\delta_m)/2]}{\sin(A/2)} = \dfrac{\sin 45^\circ}{\sin 30^\circ} = \dfrac{1/\sqrt2}{1/2} = \sqrt2 \approx 1.41.$
Five lines before the exam
- Dispersion = refractive index varies with wavelength; white light splits into VIBGYOR.
- A prism works (slab does not) because its inclined faces keep the colours separated.
- Thin prism: $\delta = (n-1)A$; since $n_v > n_r$, $\delta_v > \delta_r$ (violet most, red least).
- Angular dispersion $= (n_v - n_r)A$ (an angle); dispersive power $\omega = \dfrac{n_v - n_r}{n_y - 1}$ (dimensionless, independent of $A$).
- Rayleigh scattering $I \propto 1/\lambda^4$: blue sky, red Sun at sunrise/sunset, white clouds.