Tyndall effect is observed when:

We begin with the basic fact that the Tyndall effect refers to the scattering of a beam of light by colloidal particles present in a dispersion. This scattering makes the path of the light visible when it passes through the colloidal system.

For such scattering to be appreciable, the size of the dispersed particles plays a crucial role. Let us denote the wavelength of the visible light that we shine through the system by $$\lambda$$. Typical visible light wavelengths range roughly from $$400\ \text{nm}$$ (violet) to $$700\ \text{nm}$$ (red).

According to classical scattering theory—often introduced via Rayleigh and Mie considerations—the intensity of scattered light depends strongly on the ratio of the particle diameter, say $$d$$, to the wavelength $$\lambda$$. The salient points can be summarized qualitatively as follows:

1. If $$d \ll \lambda$$ (that is, $$d << \lambda$$), the particles are far too small to scatter visible light effectively; the system tends toward transparency and the Tyndall effect is weak or absent.

2. If $$d \gg \lambda$$ (that is, $$d >> \lambda$$), the particles are so large that the medium behaves almost like a coarse suspension rather than a colloid. In such a case, the beam of light gets mostly blocked or diffusely reflected, again not showing the characteristic Tyndall cone of a true colloid.

3. If the particle diameter $$d$$ is of the same order of magnitude as the wavelength $$\lambda$$, specifically

$$d \approx \lambda,$$

then efficient scattering occurs. Under this condition the path of light inside the medium becomes visible as a bright cone, which is precisely what we call the Tyndall effect.

Now we examine each option in the problem statement in light of the above reasoning:

A. “The diameter of dispersed particles is much larger than the wavelength of light used.”
This corresponds to $$d \gg \lambda$$. As discussed, such large particles lead more to a suspension-like behavior than to the characteristic Tyndall scattering of a colloid, so this option is incorrect.

B. “The diameter of dispersed particles is much smaller than the wavelength of light used.”
Here $$d \ll \lambda$$, which results in negligible scattering and thus a negligible Tyndall effect. Hence, this option is also incorrect.

C. “The refractive index of dispersed phase is greater than that of the dispersion medium.”
While a difference in refractive indices can influence scattering intensity, it is not the primary deciding condition for observing the Tyndall effect. Colloids can still exhibit the effect even if the refractive index of the dispersed phase is lower than that of the medium, provided the particle size condition is met. Therefore, this statement is not the key criterion asked for.

D. “The diameter of dispersed particles is similar to the wavelength of light used.”
This directly states $$d \approx \lambda$$, the precise condition under which Tyndall scattering becomes prominent. This aligns perfectly with the theoretical requirement we derived above. Hence, this statement correctly identifies when the Tyndall effect is observed.

By the process of elimination and by matching with the theory, we find that only Option D satisfies the necessary condition for the Tyndall effect.

Hence, the correct answer is Option D.