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Concepts of Physics  by H. C. Verma
Concepts of Physics

Class 11

HC Verma Part I

1

Chapter 1: Introduction to Physics

35 questions

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2

Chapter 2: Physics and Mathematics

60 questions

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3

Chapter 3: Rest and Motion: Kinematics

88 questions

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4

Chapter 4: The Forces

33 questions

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5

Chapter 5: Newton's Law of Motion

82 questions

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6

Chapter 6: Friction

57 questions

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7

Chapter 7: Circular Motion

63 questions

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8

Chapter 8: Work and Energy

101 questions

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9

Chapter 9: Centre of Mass, Linear momentum Collision

119 questions

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10

Chapter 10: Rotational Mechanics

149 questions

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11

Chapter 11: Gravitation

80 questions

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12

Chapter 12: Simple Harmonic Motion

111 questions

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13

Chapter 13: Fluid Mechanics

81 questions

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14

Chapter 14: Some Mechanical Properties of Matter

87 questions

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15

Chapter 15: Wave Motion and Waves on a String

96 questions

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16

Chapter 16: Sound Waves

118 questions

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17

Chapter 17: Light Waves

79 questions

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18

Chapter 18: Geometrical optics

123 questions

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19

Chapter 19: Optical Instruments

52 questions

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20

Chapter 20: Dispersion and Spectra

27 questions

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21

Chapter 21: Speed of Light

14 questions

22

Chapter 22: Photometry

38 questions

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Question
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Solving time: 2 mins

In the original Fizeau method, the light travelled 8.6 km and then returned. What could be the difficulty if this distance is taken as 8.6 m?

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There is no difficulty if the distance travelled by light is decreased. In this method, light has to travel a large distance of 8.6 km. So, the intensity of the light decreases considerably and the final image becomes dim. If somehow this distance is decreased, the final image is dark due to the increased light intensity.
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Question 2
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Title: Density of Electrons in a Two-Dimensional Tight-Binding Model Consider a two-dimensional tight-binding model in a square lattice with surface S and lattice spacing a. The model yields a dispersion relation for electrons of the form: E(kx, ky) = B - 2Acos(kxa) - 2Acos(kya) (1) Here, B is the local energy in each of the potential wells, and A is the coupling between first neighbors in the square lattice. Let's assume that B = 4A, so that E(0,0) = 0.
  1. Calculate the density of electronic states, g, for small values of kx and ky, such that ka << 1 and kya << 1. Hint: To work in this limit, you have to approximate the electronic dispersion relation by a quadratic function of the form E(kx, ky) = C(k^2 + k^2).
  2. Assume that electrons in the lattice are at temperature T and chemical potential μ. Calculate the density of electrons in the small wavevector limit considered in part (i).
  3. Assume that electrons in the lattice are at temperature T. Assume that the chemical potential is μ = 0. Calculate the average electron energy in the small wavevector limit considered in part (i). Hints: (1) To calculate the average electron energy, you need to calculate the total energy first and then divide it by the total number of electrons. (2) fdx + T = 2/12.
  4. In the previous parts, you have been assuming a small wavevector limit (kxa < 1, kya < 1). If the temperature is too high, this approximation will not be valid because electrons will be excited to high-energy states with large wavevectors. Consider the case μ = 0 and use the result in part (iii) to predict for what temperature the small wavevector limit will cease to be a valid approximation.
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Question Text
In the original Fizeau method, the light travelled 8.6 km and then returned. What could be the difficulty if this distance is taken as 8.6 m?
TopicRay Optics and Optical Instruments
SubjectPhysics
ClassClass 12
Answer TypeText solution:1
Upvotes95