For a prism of prism angle $\theta=60^{\circ}$, the refractive indices of the left half and the right half are, respectively, $n_1$ and $n_2\left(n_2 \geq n_1\right)$ as shown in the figure. The angle of incidence $i$ is chosen such that the incident light rays will have minimum deviation if $n_1=n_2=n=1.5$. For the case of unequal refractive indices, $n_1=n$ and $n_2=n+\Delta n$ (where $\Delta n \ll n$ ), the angle of emergence $e=i+\Delta e$.
Which of the following statement($s$) is (are) correct?
$(A)$ The value of $\Delta e$ (in radians) is greater than that of $\Delta n$
$(B)$ $\Delta e$ is proportional to $\Delta n$
$(C)$ $\Delta e$ lies between 2.0 and 3.0 milliradians, if $\Delta n=2.8 \times 10^{-3}$
$(D)$ $\Delta e$ lies between 1.0 and 1.6 milliradians, if $\Delta n=2.8 \times 10^{-3}$
