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Refraction And Dispersion Of Light Through A Prism MCQ - Practice Questions with Answers

Edited By admin | Updated on Sep 25, 2023 25:23 PM | #NEET

Quick Facts

  • Refraction Through A Prism 1, Refraction Through A Prism 2, Dispersion Of Light 1 is considered one of the most asked concept.

  • 53 Questions around this concept.

Solve by difficulty

A ray of light is incident at an angle of 60 on one face of a prism of angle 30. The emergent ray of light makes an angle of 30 with the incident ray. The angle made by the emergent ray with the second face of the prism will be:

Concepts Covered - 4

Refraction Through A Prism 1

A prism is a transparent medium whose refracting surfaces are not parallel but are inclined to each other at an angle A which is also known as angle of the prism.

The angle of deviation (\delta)-It is the angle between the emergent and the incident ray.

For the above figure  \begin{array}{l}{\delta=\left(i-r_{1}\right)+\left(e-r_{2}\right) \text { or } \delta=i+e-\left(r_{1}+r_{2}\right)} \end{array}

and using Using \ \ A=r_1+r_2 \ \ we \ \ get \ \ \delta =i+e-A

Note-From the above formula, we can say that if we interchange i and e then also we will get the same value of \delta.

  • The plot of \delta \ \ vs \ \ i

As shown in the above figure  The graph is a parabola.

If we vary i between 0^0 \ \ to \ \ 90 ^0

then  for \ \ 0 < i < e the value of \delta decreases 

and for \ \ e < i < 90 the value of \delta increases

And  when i=e \ \ then \ \ \delta =\delta _{min}

and when i=90^0 \ \ or \ \ e=90^0 \ \ \ \ then \ \ \delta =\delta _{max}

  • Grazing Incidence-When i = 90°, the incident ray grazes along the surface of the prism. This is known as grazing incidence.
  • Grazing Emergence- When e = 90°, the emergent ray grazes along the prism surface. This is known as grazing emergence.

        This happens when the light ray strikes the second face of the prism at the critical angle for glass - air.  

        I.e \ \ when \ \ \ \ r _2=\theta _c \ \ then \ \ \ e=90^0

       I.e  For the prism of refractive index \mu places in the air.

   then  i=\sin ^{-1}[\sqrt{\mu ^{2}-1} \sin A-\cos A] then e = 90°

 

 

 

Refraction Through A Prism 2

Refractive index of prism (μ)in che  case minimum deviation condition-
As we learned The angle of deviation (δ) for the prism is given as δ=i+eA and from The plot of δ vs i we get i=e then δ=δmin 

 i.e δmin=i+eA=i+iA=2iAi=A+δmin2
 

For the prism of refractive index μplaces in the air. 
For the first surface, we can write 1sini=μsinr1
similarly For the second surface, we can write μsinr2=1sine
using i=e we get r1=r2

A=r1+r2=2r1r1=A2


So 1sini=μsinr1 will give us

1sin(A+δmin2)=μsin(A2)μ=sin(A+δmin2sin(A2)

- For thin films (i.e A and δmin are small)

Then

sin(A+δmin2)=A+δmin2


 and sin(A2)=A2
 

So we get

μ=A+δminAδmin=A(μ1)

- condition of no emergence-
i.e A ray of light incidence on a prism of angle A \& Refractive index μ will not emerge out of a prism

This will happen when A>2θc
where θc= critical angle

 

 

Dispersion Of Light 1

 

Dispersion of light -The splitting of white light into its constituent colors or wavelengths is called dispersion of light.

or

angular splitting of a ray of white light into a number of components and spreading in different directions is called diversion of light.

This phenomenon arises due to the fact that the refractive index varies with wavelength. 

When white light is incident on the prism it will split itself into its constituent colors as shown in the below figure.

The deviation is given as δ=(μ1)A
Since μviolet >μred 
So δviolet >δred 
- Angular dispersion ( θ )-Angular separation between extreme colors

 i.e θ=δVδR=(μVμR)A


It depends upon μ and A .
- Dispersive power ( ω )- Ratio of angular dispersion to mean deviation.

ω=δvδrδ

where there δ is deviation of mean ray (especially yellow)
usingδv=(μv1)A,δr=(μr1)A
we get ω=μvμrμy1 where μy=μvμr2
where
μv= Refractive index of violet
μr= Refractive index of red

μy= Refractive index of yellow

 

 

Dispersion Of Light 2

Condition for deviation without dispersion-

This means an achromatic combination of two prisms in which net(or) resultant dispersion is 0, but and deviation is produced as shown in the below figure.

 

For the two prisms,

θnet =0θ1+θ2=0(μvμr)A+(μvμr)A=0A=(μvμr)Aμvμr

where
μv= Refractive index of violet ( prism 1)
μr= Refractive index of red ( prism 1)
μv= Refractive index of violet ( prism 2)
μr= Refractive index of red ( prism 2)
Similarly
For the two prisms,

θnet =0θ1+θ2=0ωδ+ωδ=0δ=δωωδnet =δ+δ=δ[1ωω]
 

where ω and ω are the dispersive powers of the two prisms and their corresponding mean deviations are δ and δ.

Condition for Dispersion without deviation-
A combination of two prisms in which deviation produced for the mean ray by the first prism is equal and opposite to that produced
by the second prism will give a dispersion of light without deviation.
This combination of two prisms is also called a direct vision prism.

 i.e δnet =0 while θnet 0
 

 

As shown in the above figure as emergent rays from the second prism is parallel to the incident white ray of the prism 1.
this will give δnet =0.
For zero deviation ,

 i.e δnet =0( i.e δ+δ=0)(μy1)A+(μy1)A=0A=(μy1)A(μy1)

and the Angular dispersion is given as

θnet=θ1+θ2=(ωδ+ωδ)=(ωδωδ)=θ(1ωω)
 

 

 

 

 

 

Study it with Videos

Refraction Through A Prism 1
Refraction Through A Prism 2
Dispersion Of Light 1

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