#engineering physics
- What is Rayleigh’s criterion of resolution? Define resolving power of grating? According to the Rayleigh’s criterion, two closely spaced point sources of light are said to be just resolved by an optical instrument only... 2
- Why the Newton’s rings are circular and centre of interference pattern (reflected) is dark? In both air-wedge film and newton’s ring experiments, each fringe is the locus of points of equal thickness of the film. In newton’s ring ex... 2
- The speed of light in a vacuum is 299,792,458 meters per second.
- A step index fiber has a core diameter of 29 x10-6 m. the refractive indices of core and cladding Answer: normalised frequency V ≈ 4.05 . V = 2π a/λsqrtn₁² - n₂² Core radius a = dfrac29×10⁻⁶2 = 14.5×10⁻⁶\ m , λ = 1.3×10⁻⁶\ m . Numerical a... 1
- Derive Gauss law for static electric and magnetic field in differential and integral form Answer: for the electric field, ointvec E· dvec A = q/ε₀ (integral form) and nabla·vec E = ρ/ε₀ (differential form). For the magnetic field,... 1
- What is the highest order spectrum, which may be seen with monochromatic light of wavelength 6000 Answer: the 3rd order. Grating element: (e+d) = 1/5000\ cm = 2×10⁻⁴\ cm = 2×10⁻⁶\ m Grating equation: (e+d)sinθ = nλ . The largest possible... 1
- Explain the concept of time dilation and deduce an expression for it. A particle moving with a speed of 0.7c. Answer: a moving clock runs slow: Δ t = dfracΔ t₀sqrt1 - v²/c² . For a particle at 0.7c, rest mass : moving mass = √(1-0.49) ≈ 0.714 , i.e.... 1
- Explain the construction and working of a Transmission Electron microscope with a schematic diagram
- 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