Given that the amplitude A of scattered light is : (i) Directly proportional to the amplitude (A₀) of incident light. (ii) Directly proportional to the volume (V) of the scattering particle (iii) Inversely proportional to the distance (r) from the scattered particle (iv) Depend upon the wavelength ( λ ) of the scattered light. then:

The correct option is A ∝ 1/λ².

We can determine the dependence of the scattered amplitude on the wavelength using dimensional analysis.

Let the relation for the amplitude of the scattered light $A$ be represented as:
$A=k{A}_0^a{V}^b{r}^c{\lambda }^d$
where $k$ is a dimensionless constant of proportionality.

From the given conditions:
1. $A$ is directly proportional to the incident amplitude $A_0$, which means $a=1$.
2. $A$ is directly proportional to the volume $V$ of the scattering particle, which means $b=1$.
3. $A$ is inversely proportional to the distance $r$, which means $c=-1$.

Substituting these values of $a$, $b$, and $c$ into our equation, we get:
$A=k\frac{A_{0}V{\lambda }^d}{r}$

Now, let us determine the dimensions of each variable involved:
- The amplitude of the scattered light $\left[A\right]=L$ (unit of length)
- The amplitude of the incident light $\left[A_0\right]=L$ (unit of length)
- The volume of the scattering particle $\left[V\right]=L^3$
- The distance from the scattering particle $\left[r\right]=L$ (unit of length)
- The wavelength of light $\left[\lambda \right]=L$ (unit of length)

Substituting these dimensions into the proportionality equation:
$\left[L\right]=\frac{\left[L\right]·\left[L^3\right]·\left[L^d\right]}{\left[L\right]}$

Simplifying the right-hand side of the equation:
$L^1=L^{3+d}$

Equating the exponents of $L$ on both sides:
$1=3+d$
$d=1-3$
$d=-2$

Therefore, the dependency of amplitude on the wavelength $\lambda$ is:
$A\propto {\lambda }^{-2}$
which can be written as:
$A\propto \frac{1}{{\lambda }^2}$