All questions
- State Maxwell’s equations in differential form in a medium, in the presence of charges and currents Answer: in a medium with charge density ρ and current density vec J , Maxwell's equations in differential form are nabla·vec D = ρ , nabla·v... 1
- Describe any two methods to synthesize nanomaterials. Answer: two common methods are ball milling (a top-down method) and the sol-gel process (a bottom-up method). 1. Ball milling (top-down) Set... 1
- Describe the physical significance of gradient, Divergence and Curl Answer: the gradient of a scalar field gives the direction and rate of its fastest increase; the divergence of a vector field measures how m... 1
- If \(\vec{A}= xyi – 8xy^2z^2j + 2xyzk \). Find \( \vec{∇}\vec{A} \ at \ point (1,-2, 4)\) Answer: nabla·vec A = 506 at (1, −2, 4). Here A_x = xy , A_y = -8xy²z² , A_z = 2xyz . Taking nablavec A as the divergence nabla·vec A : nabl... 1
- Derive the expression for the Numerical aperture for a step index fiber Answer: NA = sinθ_a = sqrtn₁² - n₂² (for a fibre in air), where n₁ and n₂ are the core and cladding refractive indices. Consider a step-inde... 1
- Draw and explain energy level diagram of Nd: YAG Laser.
- Prove that x 2+y2+z2 -c2 t 2 is invariant under Lorentz transformation. Answer: substituting the Lorentz transformation into x'²+y'²+z'²-c²t'² gives back exactly x²+y²+z²-c²t² , so the quantity is invariant. Lore... 1
- What is length contraction? Derive the expression for the same? Answer: length contraction is the shortening of a moving object's length, along its direction of motion, as measured by an observer for whom... 1
- State Maxwell’s all four equations and give the significance of each Answer: Maxwell's four equations are Gauss's law for electricity, Gauss's law for magnetism, Faraday's law and the Ampère–Maxwell law. Toget... 1
- Calculate the number of modes of a step index optical fibre of diameter 40 if its core and cladding
- When a frame of reference is said to be a non-inertial frame of reference? Give an example. Answer: a frame of reference is non-inertial when it is accelerating (changing speed or direction, including rotating) relative to an inerti... 1
- What is Galilean transformation? Derive Galilean transformation equations for position and time Answer: Galilean transformation gives the coordinates of an event in one inertial frame in terms of those in another frame moving with const... 1
- Describe the fiber optics communication system with block diagram
- Given A = x2yi +(x-y) k, find ∇A Answer: nabla·vec A = 2xy Here A_x = x²y , A_y = 0 (there is no hat j term) and A_z = x - y . nabla·vec A = ∂ A_x/∂ x + ∂ A_y/∂ y + ∂ A_z/∂... 1
- If ф(x,y,z) = 3x2y - y3z 2 , Find ∇ ф at the point (-1, -2, 1). Answer: nablaφ = 12hat i - 9hat j + 16hat k at (−1, −2, 1). φ = 3x²y - y³z² and nablaφ = ∂φ/∂ xhat i + ∂φ/∂ yhat j + ∂φ/∂ zhat k . ∂φ/∂ x =... 1
- Explain the working of atomic force microscope in detail. Answer: an atomic force microscope (AFM) scans a very sharp tip, mounted on a flexible cantilever, over the sample surface; the tiny forces... 1
- A diffraction grating used at normal incidence gives a line, λ1 = 6000 A˚ in a certain order superimposed Answer: about 2778 lines per cm. Grating equation: (e+d)sinθ = nλ . The n th order of λ₁ coincides with the (n+1) th order of λ₂ at the same... 1
- What is importance of resonant cavity in the operation of laser? Answer: the resonant (optical) cavity provides optical feedback: its mirrors send photons back and forth through the active medium so that s... 1
- How is multipath dispersion overcome in Graded index fibre? Answer: in a graded-index fibre the refractive index decreases from the axis outwards, so rays that travel longer paths away from the axis a... 1
- Distinguish between single mode and multimode optical fiber Answer: a single-mode fibre has a very thin core that allows only one path (mode) of light; a multimode fibre has a wider core that allows m... 1
- Distinguish between step index and graded index optical fiber. Answer: in a step-index fibre the core has a uniform refractive index that drops suddenly at the cladding; in a graded-index fibre the core... 1
- Derive Maxwell’s third equation in integral and differential form. Given that D = 20x î +10 ĵ (C/m2 ).
- Draw the schematic diagram of Scanning Electron Microscope and explain its construction, working, advantages
- What is population inversion state? Explain its significance in the operation of LASER. Answer: population inversion is the state in which more atoms are in a higher (excited) energy level than in a lower energy level. It is ess... 1