$A$ thin prism of angle $6^{\circ}$ made of glass of refractive index $1.5$ is combined with another prism made of glass of refractive index $1.75$ to produce dispersion without deviation. Then, the angle of the second prism is (in $^{\circ}$)

Assertion: There exist two angles of incidence for the same magnitude of deviation (except for minimum deviation) by a prism kept in air.
Reason: In a prism kept in air,a ray is incident on the first surface and emerges out of the second surface. If another ray is incident on the second surface along the path of the previous emergent ray,then this ray emerges out of the first surface along the path of the previous incident ray. This principle is called the principle of reversibility of light.

The refractive index of glass for red light is $1.520$ and for blue light is $1.525$. Let $D_1$ and $D_2$ be the angles of deviation for red and blue light,respectively,in a prism of this glass. Then:

$A$ monochromatic beam of light is incident at $60^{\circ}$ on one face of an equilateral prism of refractive index $n$ and emerges from the opposite face making an angle $\theta(n)$ with the normal (see the figure). For $n=\sqrt{3}$ the value of $\theta$ is $60^{\circ}$ and $\frac{d \theta}{d n}=m$. The value of $m$ is

The prism angle of a prism is $40^{\circ}$. $A$ light ray is incident at $38^{\circ}$ and undergoes minimum deviation. The angle of minimum deviation is ........$^{\circ}$.

$A$ thin prism $P_1$ with an angle $6^{\circ}$ and made of glass of refractive index $1.54$ is combined with another prism $P_2$ made from glass of refractive index $1.72$ to produce dispersion without average deviation. The angle of prism $P_2$ is $........{}^{\circ}$