Question 1

The equation ω=μ−1μu​−μr​​ was derived for a prism having small refracting angle. Is it also valid for a prism of large refracting angle? Is it also valid for a glass slab or a glass sphere?

Accepted Answer

Dispersive power depends on angular deviation, and angular deviation is valid only for a small refracting angle and a small angle of incidence. Therefore, dispersive power is not valid for a prism of large refracting angle. It is also not valid for a glass slab or a glass sphere, as it has a large refracting angle.

Question 2

Can the dispersive power ω=μ−1μu​−μr​​ be negative? What is the sign of ω if a hollow prism is immersed into water?

Accepted Answer

No, it cannot be negative, as the refractive index for violet light is always greater than that for red light. Also, refractive index is inversely proportional to λ2. The sign of ω will be positive, as μ is still greater than 1 and as μv​>μr​.

Question 3

If three identical prisms are combined, is it possible to pass a beam that emerges undeviated? Undispersed?

Accepted Answer

No, it is not possible even when prisms are be combined with their refractive angle reversed with respect to each other. There will be at least a net deviation and dispersion equal to the dispersion and deviation produced by a single prism.

Question 4

Monochromatic light should be used to produce pure spectrum. Comment on this statement.

Accepted Answer

No, monochromatic light cannot be used to produce a pure spectrum. A spectrum is produced when a light of different wavelengths is deviated through different angles and gets separated. Monochromatic light, on the other hand, has a single wavelength.

Question 5

Does focal length of a lens depend on the colour of the light used? Does focal length of a mirror depend on the colour?

Accepted Answer

Yes, the focal length of a lens depends on the colour of light.According to lens-maker's formula,f1​=(μ−1)(R1​1​−R2​1​)Here, f is the focal length, μ is the refractive index, R is the radius of curvature of lens.The refractive index (μ) depends on the inverse of square of wavelength.The focal length of a mirror is independent of the colour of light.

Question 6

Suggest a method to produce a rainbow in your house.

Accepted Answer

A rainbow can be produced using a prism. Another way of producing a rainbow is to dip a mirror inside water, keeping it inclined along the wall of a tumbler. The light coming from water after reflecting from the mirror will give a rainbow.

Question 7

The angular dispersion produced by a prism ___________ .

Accepted Answer

(a) Increases if the average refractive index increases.If μ is the average refractive index and A is the angle of prism, then the angular dispersion produced by the prism is given by δ=(μ−1)A.

Question 8

If a glass prism is dipped in water, its dispersive power ___________ .

Accepted Answer

(b) Decreases.If μ is the refractive index and A is the angle of prism, then the angular dispersion produced by the prism will be given by δ=(μ−1)A.Because the relative refractive index of glass with respect to water is small compared to the refractive of glass with respect to air, the dispersive power of the glass prism is more in air than that in water.

Question 9

A prism can produce a minimum deviation δ in a light beam. If three such prisms are combined, the minimum deviation that can be produced in this beam is _______________.

Accepted Answer

(b) δ.In combination (refractive angles of prisms reversed with respect to each other), the deviations through two prisms cancel out each other and the net deviation is due to the third prism only.

Question 10

Consider the following two statements :-(A) Line spectra contain information about atoms.(B) Band spectra contain information about molecules.

Accepted Answer

(d) Both A and B are correct.Because line spectra contain wavelengths that are absorbed by atoms and band spectra contain bunch wavelengths that are absorbed by molecules, both statements are correct.

Question 11

The focal length of a converging lens arefv​ andfr​ for violet and red light respectively.

Accepted Answer

(c) fv​<fr​.Focal length is inversely proportional to refractive index and refractive index is inversely proportional to λ2. So, keeping other parameters the same, we can say:f∝λ21​...........(∵  λr​ < λv​)∴fv​<fr​

Question 12

A narrow beam of white light goes through a slab having parallel faces.

Accepted Answer

(b) The emergent beam is white.(c) The light inside the slab is split into different colours.White light will split into different colours inside the glass slab because the value of refractive index is different for different wavelengths of light; thus, they suffer different deviations. But the emergent light will be white light. As the faces of the glass slide are parallel, the emerging lights of different wavelengths will reunite after refraction.

Question 13

By properly combining two prisms made of different materials, it is possible to:

Accepted Answer

(a) Have dispersion without average deviation(b) have deviation without dispersion(c) have both dispersion and average deviation.Consider the case of prisms combined such that the refractive angles are reversed w.r.t. each other. Then, the net deviation of the yellow ray will be δy​ =(μy​ −1)A−(μy′​−1)A′And, the net angular dispersion will beδy​ − δr​ =(μy​−1)A(ω−ω′)Thus, by choosing appropriate conditions, we can have the above mentioned cases.

Question 14

In producing a pure spectrum, the incident light is passed through a narrow slit placed in the focal plane of an achromatic lens because a narrow slit ___________ .

Accepted Answer

(d) Allows a more parallel beam when it passes through the lens.To produce a pure spectrum, a parallel light beam is required to be incident on the dispersing element. So, the incident light is passed through a narrow slit placed in the focal plane of an achromatic lens.

Question 15

Which of the following quantities related to a lens depend on the wavelength or wavelengths of the incident light?

Accepted Answer

(a) Power(b) Focal length(c) Chromatic aberrationThe focal length, power and chromatic aberration are dependent on the refractive index of the lens, which itself is dependent on the wavelength of the light.

Question 16

Which of the following quantities increase when wavelength is increased? Consider only the magnitudes.

Accepted Answer

(b) The focal length of a converging lens(d) The focal length of a diverging lens.The focal length of a lens is inversely proportional to the refractive index of the lens and the refractive index of the lens is inversely proportional to the square of wavelength. Therefore, the focal length is directly dependent on wavelength; it increases when the wavelength is increased.

Question 17

A flint glass prism and a crown glass prism are to be combined in such a way that the deviation of the mean ray is zero. The refractive index of flint and crown glasses for the mean ray are 1.620 and 1.518 respectively. If the refracting angle of the flint prism is 6.0°, what would be the refracting angle of the crown prism?

Accepted Answer

Given:Refractive index of the flint glass, μf​  = 1.620Refractive index of the crown glass, μc​  = 1.518Refractive angle of the flint prism, Af​  = 6°Now,Let the refractive angle of the crown prism be Ac​ .For the net deviation of the mean ray to be zero,Deviation by the flint prism = Deviation by the crown prismi.e., (μf​ − 1)Af​  = (μc​ − 1)Ae​ ⇒ Ac​ =(μe​−1μf​−1​)Af​⇒ Ac​ =(1.518−11.620−1​)×6.0∘=7.2∘Thus, the refracting angle of the crown prism is 7.2°.

Question 18

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° made of this material.

Accepted Answer

Given:Refractive index for red light,μr​  = 1.56Refractive index for yellow light, μy​ = 1.60Refractive index for violet light, μv​  = 1.68Angle of prism, A = 6°(a)  Dispersive power (ω) is given byω=μy​−1μv​−ur​​ On substituting the values in the above formula, we getω=(1.60−1)(1.68−1.56)​=0.600.12​=0.2(b) Angular dispersion ==0.600.12​=0.2 (μv​−μr​) =0.600.12​=0.2 =0.600.12​=0.2 A  =(0.12) × 6° = 0.72°Thus, the angular dispersion produced by the thin prism is 0.72°.

Question 19

The focal lengths of a convex lens for red, yellow and violet rays are 100 cm, 98 cm and 96 cm respectively. Find the dispersive power of the material of the lens.

Accepted Answer

Focal lengths of the convex lens:For red rays, fr​ =100 cmFor yellow rays, fy​ =98 cmFor violet rays, fv​ =96 cmLetμr​ = Refractive index for the red colourμy​ = Refractive index for the yellow colourμv​ = Refractive index for the violet colourFocal length of a lens (f) is given byf1​=(μ−1)(R1​1​−R2​1​)Here, μ is the refractive index and R1​ and R2​ are the radii of curvatures of the lens.Thus, we have(μ−1)=f1​×(R1​1​−R2​1​)1​⇒ (μ−1)=fk​...........[k=(R1​1​−R2​1​)1​]For red rays, μr​ −1=100k​For yellow rays, μy​ −1=98k​,For violet rays, μv​ −1=96k​Dispersive power (ω) is given by ω=μy​−1μv​−μr​​Substituting the values, we getω=(μy​−1)(μv​−1)−(μr​−1)​⇒ω=0.0408Thus, the dispersive power of the material of the lens is 0.0408.

Question 20

The refractive index of a material changes by 0.014 as the colour of the light changes from red to violet. A rectangular slab of height 2.00 cm made of this material is placed on a newspaper. When viewed normally in yellow light, the letters appear 1.32 cm below the top surface of the slab. Calculate the dispersive power of the material.

Accepted Answer

Given:Difference in the refractive indices of violet and red lights = 0.014Let μv and μr be the refractive indices of violet and red colours.Thus, we have:μv​ −μr​= 0.014Now,Real depth of the newspaper = 2.00 cmApparent depth of the newspaper = 1.32 cmRefractive index =Apparent depthReal depth​ Refractive index for yellow light (μy​) is given byμy​ =1.322.00​=1.515Also,Dispersive power, ω=μy​−1μv​−μr​​=1.515−10.014​Or, ω=0.5150.014​=0.027 Thus, the dispersive power of the material is 0.027.

Chapter 20 : Dispersion and Spectra