H C Verma solutions, Dispersion and Spectra, QUESTIONS FOR SHORT ANSWER, Chapter-20, Concepts of Physics, Part-I

Dispersion and Spectra

QUESTIONS FOR SHORT ANSWER

1. The equation ⍵ = (µᵥ-µᵣ)/(µ-1) was derived for a prism having a small refracting angle. It is also valid for a prism of large refracting angle? Is it also valid for a glass slab or a glass sphere?

Answer: The given equation is derived assuming the refracting angle A to be small so that

Sin(A+ẟ)/2 ≈(A+ẟ)/2 and

Sin(A/2) ≈ A/2.

So it is not valid for a prism of large refracting angle. 

For a glass sphere, the refracting angle will be large. Hence it is not valid for a glass sphere.

For a glass slab, the refracting angle A=0. But,

ẟ = (µ-1)A = 0. So this equation for ⍵ cannot be derived for A = 0.

2. Can the dispersive power ⍵ = (µᵥ-µᵣ)/(µ-1) be negative? What is the sign of ⍵ if a hollow prism is immersed in water?     

Answer: In the equation  ⍵ =(µᵥ -µᵣ)/(µ-1)

µᵥ is always greater than µᵣ for the transparent prism kept in a medium having a lesser refractive index than it. So µᵥ-µᵣ > 0. Also µ > 1, so µ-1 >0. Hence the dispersive power ⍵ will be positive. 

         If a hollow prism is immersed in water the equation of the dispersive power will become

⍵ = (1/µᵥ -1/µᵣ)/(1/µ-1)

So both the numerator and the denominator will become negative and we will get ⍵ positive.

          So in normal situations ⍵ will not be negative.

   

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

Answer: Since the prisms are identical, they can be combined in two ways - First, having each one's vertex near each other (at the top) and second, two vertices and one base on the top. 

      The first case will make it a prism with the refracting angle three times larger. So there will be a deviation as well as dispersion.

Diagram for Q-3

       The second case will make it a similar prism to one of the identical prisms with the same refracting angle. So in this case also there will be a deviation and the dispersion.

        Hence the answer is "No". 

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

Answer: The spectrum is obtained on a white wall or paper when different wavelengths of light get deviated through different angles by a dispersing element. When no two colors overlap each other in this spectrum, it is called a pure spectrum. If monochromatic light is used there will be only one color, not a spectrum. 

5. Does the focal length of a lens depend on the color of the light used? Does the focal length of a mirror depend on the color?

Answer: The focal length of a lens is given by the lens maker's formula

1/f =(µ-1){1/R₁ - 1/R₂}

Clearly, the focal length increases as µ decreases. µ depends on the color of the light. So the focal length of a lens depends on the color of the light.

Since there is no refraction in the mirror and it works on the laws of reflection which is the same for all colors. For example, for the same angle of incidence, the angle of reflection will be the same for all colors. Hence the focal length of a mirror does not depend on the color of the light.   

6. Suggest a method to produce a rainbow in your house.

Answer: The principle behind making a rainbow is to disperse the white light. One method to make a rainbow inside a room is to allow a narrow beam of light to fall on a surface of the water in a glass. For this sunray is allowed to make a narrow beam from a  partly closed window. Transparent glass is filled with clear water and a paper with a slit is glued to the upper portion of the glass. The glass is placed such that the sun rays fall on the slit and the emerging light is allowed to fall on a white paper. We get a rainbow on the paper. See the diagram below.

Diagram for a rainbow.

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CHAPTER- 19 - Optical Instruments

Questions for Short Answers

OBJECTIVE-I

OBJECTIVE-II

EXERCISES - Q 1 to Q 12

EXERCISES - Q 13 to Q 24

CHAPTER- 18 - Geometrical Optics

Questions for Short Answers

OBJECTIVE-I

OBJECTIVE-II

EXERCISES - Q 1 to Q10

EXERCISES- Q11 to Q20

EXERCISES- Q21 to Q30

EXERCISES- Q31 to Q40

EXERCISES- Q41 to Q50

EXERCISES- Q51 to Q60

EXERCISES- Q61 to Q70

EXERCISES- Q71 TO 79

CHAPTER- 17 - Light Waves

Questions for Short Answers

OBJECTIVE - I

OBJECTIVE - II

EXERCISES - Q1-Q10

EXERCISES - Q11-Q20

EXERCISES - Q21-Q30

EXERCISES - Q31-Q41

CHAPTER- 16 - Sound Waves

Questions for Short Answers

OBJECTIVE-I

OBJECTIVE-II

EXERCISES - Q-1 TO Q-10

EXERCISES - Q-11 TO Q-20

EXERCISES -Q-21 TO Q-30

EXERCISES -Q-31 TO Q-40

EXERCISES -Q-41 TO Q-50

EXERCISES -Q-51 TO Q-60

EXERCISES -Q-61 TO Q-70

EXERCISES - Q-71 TO Q-80

EXERCISES - Q-81 TO Q-89

CHAPTER- 15 - Wave Motion and Waves on a String

Questions for Short Answers

OBJECTIVE-I

OBJECTIVE-II

EXERCISES - Q-1 TO Q-10

EXERCISES - Q-11 TO Q-20

EXERCISES - Q-21 TO Q-30

EXERCISES - Q-31 TO Q-40

EXERCISES - Q-41 TO Q-50

EXERCISES - Q-51 TO Q-57

CHAPTER- 14 - Fluid Mechanics

Questions for Short Answers

OBJECTIVE-I

OBJECTIVE-II

EXERCISES- Q-1 TO Q-10

EXERCISES- Q-11 TO Q-20

EXERCISES- Q-21 TO Q-32

CHAPTER- 13 - Fluid Mechanics

Questions for Short Answers

OBJECTIVE-I

OBJECTIVE-II

EXERCISES Q-1 TO Q-10

EXERCISES- Q11 TO Q20

EXERCISES Q-21 TO Q30

EXERCISES Q-31 TO Q35

CHAPTER- 12 - Simple Harmonic Motion

Questions for Short Answers

OBJECTIVE-I

OBJECTIVE-II

EXERCISES- Q1 TO Q10

EXERCISES- Q11 TO Q20

EXERCISES- Q21 TO Q30

EXERCISES- Q31 TO Q40

EXERCISES- Q41 TO Q50

EXERCISES- Q51 TO Q58 (2-Extra Questions)

CHAPTER- 11 - Gravitation

Questions for Short Answers

OBJECTIVE - I

OBJECTIVE - II

EXERCISES - Q_1 to Q_10

EXERCISES -Q-11 TO Q-20

EXERCISES -Q 21 TO 30

EXERCISES -Q 31 TO 39

CHAPTER- 10 - Rotational Mechanics

Questions for Short Answers

OBJECTIVE - I

OBJECTIVE - II

EXERCISES - Q-1 TO Q-15

EXERCISES - Q-16 TO Q-30

EXERCISES Q-31 TO Q-45

EXERCISES Q-46 TO Q-60

EXERCISES Q-61 TO Q-75

EXERCISES Q-76 TO Q-86

CHAPTER- 9 - Center of Mass, Linear Momentum, Collision

Questions for Short Answers

Objective - I

Objective - II

EXERCISES Q-1 TO Q-10

EXERCISES Q-11TO Q-20

EXERCISES Q-21 TO Q-30

EXERCISES Q-31 TO Q-42

EXERCISES Q-43 TO Q-54

CHAPTER- 8 - Work and Energy

Click here for → Question for Short Answers

Click here for → OBJECTIVE-I

Click here for → OBJECTIVE-II

Click here for → Exercises (1-10)

Click here for → Exercises (11-20)

Click here for → Exercises (21-30)

Click here for → Exercises (31-42)

Click here for → Exercise(43-54)

CHAPTER- 7 - Circular Motion

Click here for → Questions for Short Answer 

Click here for → OBJECTIVE-I

Click here for → OBJECTIVE-II

Click here for → EXERCISES (1-10)

Click here for → EXERCISES (11-20)

Click here for → EXERCISES (21-30)

CHAPTER- 6 - Friction

Click here for → Questions for Short Answer

Click here for → OBJECTIVE-I

Click here for → Friction - OBJECTIVE-II

Click here for → EXERCISES (1-10)

Click here for → Exercises (11-20)

Click here for → EXERCISES (21-31)

For more practice on problems on friction solve these- "New Questions on Friction".

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CHAPTER- 5 - Newton's Laws of Motion

Click here for → QUESTIONS FOR SHORT ANSWER

Click here for→ Newton's laws of motion - Objective - I

Click here for → Newton's Laws of Motion - Objective -II

Click here for → Newton's Laws of Motion-Exercises(Q. No. 1 to 12)

Click here for→Newton's Laws of Motion,Exercises(Q.No. 13 to 27)

Click here for→Newton's Laws of Motion,Exercises(Q.No. 28 to 42)

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CHAPTER- 4 - The Forces

The Forces-

"Questions for short Answers"    

Click here for "The Forces" - OBJECTIVE-I

Click here for "The Forces" - OBJECTIVE-II

Click here for "The Forces" - Exercises

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CHAPTER- 3 - Kinematics - Rest and Motion

Click here for "Questions for short Answers"

Click here for "OBJECTIVE-I"

Click here for EXERCISES (Question number 1 to 10)

Click here for EXERCISES (Question number 11 to 20)

Click here for EXERCISES (Question number 21 to 30)

Click here for EXERCISES (Question number 31 to 40)

Click here for EXERCISES (Question number 41 to 52)

CHAPTER- 2 - "Vector related Problems"

Click here for "Questions for Short Answers"

Click here for "OBJECTIVE-I

Click here for "OBJECTIVE-II"

Click here for "Exercises"