White light is passed through a prism of angle $5^{\circ}$. If the refractive indices for red and blue colors are $1.641$ and $1.659$ respectively,the angular dispersion between them will be..... (in $^{\circ}$)

$A$ ray of light passing through a prism $(\mu = \sqrt{3})$ suffers minimum deviation. It is found that the angle of incidence is double the angle of refraction within the prism. Then,the angle of prism is ..... (in degrees).

Find the value of the angle of emergence for an emergent ray from the prism in the figure given below. (Refractive index of the material of the prism is $\sqrt{3}$ and the refractive index of air is $1$) (in $^\circ$)

Consider the following statements for the refraction of light through a prism,when the angle of deviation is minimum.
$(A)$ The refracted ray inside the prism becomes parallel to the base.
$(B)$ Larger angle prisms provide smaller angle of minimum deviation.
$(C)$ The angle of incidence and the angle of emergence become equal.
$(D)$ There are always two sets of angles of incidence for which the deviation will be the same,except at the minimum deviation setting.
$(E)$ The angle of refraction becomes double the prism angle.
Choose the correct answer from the options given below.

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 $\Delta n=2.8 \times 10^{-3}$

$A$ prism with a refractive index of $1.53$ is placed in water with a refractive index of $1.33$. If the angle of the prism is $60^{\circ}$,then the angle of minimum deviation in water will be ....$^{\circ}$.