$A$ parallel beam of monochromatic light is incident at one surface of an equilateral prism. The angle of incidence is $55^o$ and the angle of emergence is $46^o$. The angle of minimum deviation will be:

$A$ ray of light is incident on an equilateral glass prism placed on a horizontal table. For minimum deviation,which of the following is true?

Two thin prisms of flint glass, with refracting angles of $6^o$ and $8^o$ respectively, possess dispersive powers in the ratio

As shown in the diagram, when the incident ray is parallel to the base of the prism, the emergent ray grazes along the second surface. If the refractive index of the material of the prism is $\sqrt{2}$, the angle $\theta$ of the prism is: (in $^{\circ}$)

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 $n_2$ $(n_2 \geq n_1)$ 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 $\Delta n=2.8 \times 10^{-3}$

Derive ${D_m} = A({n_{21}} - 1)$ for a thin prism.