A thin prism is made of a material having refractive indices 1.61 and 1.65 for red and violet light. The dispersive power of the material is 0.07. It is found that a beam of yellow light passing through the prism suffers a minimum deviation of ${4.0}^{\circ}$ in favourable conditions. Calculate the angle of the prism.

Open in App

Solution

Given that : $μ_{r}$ = 1.61

$μ_{v}$ = 1.65,

$ω$ = 0.07 and $δ_{y} = 4^{\circ}$

Now $ω = \frac{μ_{v} - μ_{r}}{μ_{y} - 1}$

$0.07 = \frac{1.65 - 1.61}{μ_{y} - 1}$

$μ_{y} - 1 = \frac{0.04}{0.07} = \frac{4}{7}$

Again $δ = (μ - 1) A$

$\Rightarrow A = \frac{δ_{y}}{μ_{y} - 1} = \frac{4}{(\frac{4}{7})} = 7$

Suggest Corrections

Similar questions

A certain material has refractive indices 1.56, 1.60 and 1.68 for red, yellow and violet light respectively. (a) Calculate the dispersive power. (b) Find the angular dispersion produced by a thin prism of angle $6^{\circ}$ made of this material.

Q. If the refractive indices of a prism for red, yellow and violet colours be 1.61, 1.63 and 1.65 respectively, then the dispersive power of the prism will be:

Q. The angle of incidence for a ray of light at a refracting surface of a prism is

45^{o}

. The angle of prism is

60^{o}

. If the ray suffers minimum deviation through the prism, the angle of minimum deviation and refractive index of the material of the prism respectively, are

Q. A ray of light passing through a prism having

μ = \sqrt{2}

suffers minimum deviation. It is found that the angle of incidence is double the angle of refraction within the prism. What is the angle of prism?

Q. The minimum deviations suffered by red, yellow, and violet beams passing through an equilateral transparent prism are

{38.4}^{\circ}, {38.7}^{\circ}

and

{39.2}^{\circ}

respectively. Calculate the dispersive power of the medium.

Join BYJU'S Learning Program

Given that : μr = 1.61 μv = 1.65, ω = 0.07 and δy=4∘ Now ω=μv−μrμy−1 0.07=1.65−1.61μy−1 μy−1=0.040.07=47 Again δ=(μ−1)A ⇒ A=δyμy−1=4(47)=7