#engineering physics
- What is Rayleigh’s criterion of resolution? Define resolving power of grating? Answer: Two point sources (or spectral lines) are just resolved when the principal maximum of one falls on the first minimum of the other. R... 2
- Why the Newton’s rings are circular and centre of interference pattern (reflected) is dark? Answer: The rings are circular because each fringe is a locus of points of equal air-film thickness, and such points lie on circles centred... 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 ap... 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 v... 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. abo... 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·vec... 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: nabla·ve... 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. Loren... 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) + (∂... 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/(∂ x)hat i + ∂φ/(∂ y)hat j + ∂φ/(∂ z)hat k. ∂φ/(... 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