Prism and dispersion

In the List-I, four optical effects are mentioned. The physical phenomena of light which are essential to describe these optical effects are given in List-II. Choose the option which describes the correct match between the entries in List-I to those in List-II.

A beam of polychromatic light passes through a thin prism of prism angle $6^\circ$. The refractive index of the material of the prism varies with wavelength $(\lambda)$ as $n(\lambda)=\alpha\lambda+\dfrac{\beta}{\lambda^2}$, where $\alpha=3\ \mu\text{m}^{-1}$ and $\beta=0.096\ \mu\text{m}^2$. If $\lambda_{\min}$ is the wavelength at which the angle of minimum deviation $D_m$ is smallest, then the correct value of $D_m$ at $\lambda_{\min}$ is

Consider two isosceles prisms 1 and 2 with prism angles $A_1$ and $A_2$ and refractive indices $n_1$ and $n_2$, respectively, as shown in the figure. The faces $a_1b_1$ and $a_2b_2$ are parallel to each other and perpendicular to the mirror $M$. If a ray of light is incident on the face $a_1c_1$ and emerges from the face $a_2c_2$, then the correct statement(s) is/are:

For a thin symmetric prism made of glass (refractive index 1.5), the ratio of incident angle and minimum deviation will be ________.

One side of an equilateral prism is painted by a transparent material of refractive index $n_2$. The refractive index of prism is 1.6. The minimum value of $n_2$ required for total internal reflection from painted face is ________.

A ray of light passing through an equilateral prism is having velocity $2.12\times10^8$ m/s in the prism material, then the minimum angle of deviation is ________ degrees.

Angle of minimum deviation is equal to the half of the angle of prism in an equilateral prism. The refractive index of the prism is ________.

Two equilateral-triangular prisms P₁ and P₂ are kept with their sides parallel to each other, in vacuum, as shown in the figure. A light ray enters prism P₁ at an angle of incidence $\theta$ such that the outgoing ray undergoes minimum deviation in prism P₂. If the respective refractive indices of P₁ and P₂ are $\sqrt{\dfrac32}$ and $\sqrt3$, then $\theta = \sin^{-1}\left[\sqrt{\dfrac32}\sin\left(\dfrac{\pi}{\beta}\right)\right]$, where the value of $\beta$ is _____.

A plane polarized blue light ray is incident on a prism such that there is no reflection from the surface of the prism. The angle of deviation of the emergent ray is $\delta = 60^\circ$ (see Figure-1). The angle of minimum deviation for red light from the same prism is $\delta_{\min} = 30^\circ$ (see Figure-2). The refractive index of the prism material for blue light is $\sqrt3$. Which of the following statement(s) is(are) correct?

The refracting angle of a prism is A and refractive index of the material of the prism is $\cot(A/2)$. Then the angle of minimum deviation will be -

The refractive index of an equilateral prism is $\sqrt2$. The angle of emergence under minimum deviation position of prism, in degree, is ______.

Which of the following statement is correct ?

In the given figure, the face AC of the equilateral prism is immersed in a liquid of refractive index 'n'. For incident angle 60° at the side AC, the refracted light beam just grazes along face AC. The refractive index of the liquid $n=\dfrac{\sqrt x}4$. The value of $x$ is ______.

(Given refractive index of glass = 1.5)

A thin prism of angle 6° and refractive index for yellow light $(n_Y)$ 1.5 is combined with another prism of angle 5° and $n_Y=1.55$. The combination produces no dispersion. The net average deviation (δ) produced by the combination is $\left(\dfrac1x\right)^\circ$. The value of $x$ is ______.

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 $n_2$ $(n_2 \ge n_1)$ 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 monochromatic light is incident from air on a refracting surface of a prism of angle 75° and refractive index $n_0 = \sqrt3$. The other refracting surface of the prism is coated by a thin film of material of refractive index $n$ as shown in figure. The light suffers total internal reflection at the coated prism surface for an incidence angle of $\theta \le 60^\circ$. The value of $n^2$ is ______.

For an isosceles prism of angle $A$ and refractive index $\mu$, it is found that the angle of minimum deviation $\delta_m = A$. Which of the following options is/are correct?

In an experiment for determination of refractive index of glass of a prism by $i-\delta$, plot, it was found that a ray incident at angle 35°, suffers a deviation of 40° and that it emerges at angle 79°. In that case which of the following is closest to the maximum possible value of the refractive index ?

A monochromatic beam of light is incident at 60° 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 $n=\sqrt3$ the value of $\theta$ is 60° and $\dfrac{d\theta}{dn}=m$. The value of $m$ is

Monochromatic light is incident on a glass prism of angle A. If the refractive index of the material of the prism is μ, a ray, incident at an angle θ, on the face AB would get transmitted through the face AC of the prism provided :