#mu engineering
- Derive an expression for acceptance angle of a step index optical fiber. Set-up: A step-index fibre has a core of index n₁ and a cladding of index n₂ ( n₁>n₂ ). Light enters the core from a medium of index n₀ (air... 1
- Obtain an expression for minimum thickness of anti-reflecting film. Anti-reflecting (AR) film: A thin transparent film of index μ and thickness t coated on glass of index μ_g , with 1<μ<μ_g . R1 R2 incident (... 1
- Find Curl of vector F (x2y + xy2z + 3x2z2) at point (1,-1,1) Interpretation: The printed components are taken as vec F=x²y hat i+xy²z hat j+3x²z² hat k . nabla×vec F=beginvmatrixhat i&hat j&hat k\\ ∂_x... 1
- Derive the Schrodinger’s Time Dependent differential equation for matter waves A free particle moving along x is described by the wave function psi(x,t)=A e^(-i(Et-px)/hbar) using E=hbarω and p=hbar k . Step 1 (time der... 1
- Show that the intrinsic Fermi level lies in the middle of the band gap. In an intrinsic semiconductor, the electron concentration in the conduction band is n=N_c e^(-(E_c-E_F)/kT) and the hole concentration in th... 1
- Calculate electron and hole concentration in intrinsic silicon at room temperature if its electric conductivity is 4x10-4 mho/m. Given that mobility of electron is 0.14 m2/V-Sec mobility of holes is 0.04 m2/V-Sec. Given: σ_i=4×10⁻⁴ mho/m, μ_e=0.14 m²/V s, μ_h=0.04 m²/V s. Formula: For an intrinsic semiconductor, n=p=n_i and σ_i=n_ie(μ_e+μ_h) . n_i=σ_i/... 1
- Derive the condition for maxima due to interference of light reflected from thin film of uniform thickness. Set-up: A thin transparent film of uniform thickness t and refractive index μ is in air. A ray AB is incident at angle i . Part of it is ref... 1
- Calculate velocity and de-Broglie wavelength of alpha particle of energy 1[unit prefix partly illegible in the source scan; read as k]eV. Given: mass of alpha particle as 6.68x10-27 kg. Assumption: The energy unit is partly obscured in the scan. We read it as E=1 keV. The results for 1 MeV are given at the end. Given: E=1 ke... 1
- Explain the following terms in optical fiber: a) Total internal reflection b) Critical angle c) Acceptance angle d) Attenuation e) Numerical aperture. a) Total internal reflection (TIR): When light travels from a denser medium (core, n₁ ) to a rarer one (cladding, n₂<n₁ ) at an angle of inc... 1
- Deduce Maxwell’s second equation in differential and integral form. Maxwell's second equation is Gauss's law for magnetism. Integral form: Magnetic field lines are always closed loops, because isolated magnet... 1
- With the help of neat diagram, explain construction and working of He Ne laser. He–Ne laser is a four-level gas laser that gives a continuous output at 6328 Å (red). Construction: discharge tube (He:Ne ≈ 10:1, ~1 mm Hg)... 1
- What is metastable state? What is the role of metastable state in LASER? Metastable state: An excited energy level of an atom in which the electron stays for an unusually long time, about 10⁻³ s, compared with an... 1
- An optical fiber has an acceptance angle of 30° and core refractive index of [value not printed in the source paper] calculate refractive index of cladding? Note: The core index is missing from the printed paper. As the paper allows, we assume n₁=1.5 (a typical glass core) and take the fibre to b... 1
- Explain why an excessively thin film appears black in reflected light? For a thin film of index μ and thickness t , the effective path difference between the two reflected rays is Δ=2μ tcos r-λ/2 The extra λ/2 c... 1
- Show that the divergence of a curl of a vector is zero. Let vec A=A_xhat i+A_yhat j+A_zhat k . nabla×vec A=Big(∂ A_z/∂ y-∂ A_y/∂ zBig)hat i+Big(∂ A_x/∂ z-∂ A_z/∂ xBig)hat j+Big(∂ A_y/∂ x-∂ A_x/∂ y... 1
- State the properties of matter waves. Properties of matter waves (de Broglie waves): Wavelength λ=h/p=h/mv : lighter particles have larger wavelengths, and so do slower ones. If... 1
- An electron is bound in an 1D potential well of width 2 A° but of infinite height. Find its energy values in the ground state and in first excited state. (Given: Planck constant is 6.634x10-34 J-Sec) Given: L=2 Å =2×10⁻¹⁰ m, h=6.634×10⁻³⁴ J s, m=9.1×10⁻³¹ kg. Formula: E_n=n²h²/8mL² Ground state (n = 1): E₁=frac(6.634×10⁻³⁴)²8×9.1×10⁻³¹×(2... 1
- Write Fermi Dirac distribution function and explain the terms involved in it The Fermi–Dirac distribution function gives the probability that an available energy state E is occupied by an electron at absolute temperat... 1
- Derive an expression for numerical aperture of a step index optical fiber. Set-up: A step-index fibre has a core of index n₁ and a cladding of index n₂ ( n₁>n₂ ). Light enters the core from a medium of index n₀ (air... 1
- With the neat energy level diagram, explain the construction and working of He Ne Gas laser. He–Ne laser is a four-level gas laser that gives a continuous output at 6328 Å (red). Construction: discharge tube (He:Ne ≈ 10:1, ~1 mm Hg)... 1
- In a Newton’s ring arrangement, a drop of liquid of refractive index 1.33 is placed in between the lens and plate. The diameter of 9th dark ring is found to be 0.58 cm. Obtain the radius of curvature, if the wavelength of light is 6000 A°. Given: μ=1.33 , n=9 , D₉=0.58 cm =5.8×10⁻³ m, λ=6000 Å =6×10⁻⁷ m. Formula: For dark rings in reflected light with a liquid film, 2μ t=nλ and... 1
- What is gradient? If \(\phi=3(x^2y-y^2x)\), find \(\nabla\phi\) at the point (1, -2, -1). Gradient: The gradient of a scalar field φ(x,y,z) is the vector nablaφ=∂φ/∂ xhat i+∂φ/∂ yhat j+∂φ/∂ zhat k Its magnitude is the maximum rate... 1
- Prove that electron cannot reside inside the nucleus of an atom. Using Heisenberg's uncertainty principle: Δ x Δ p≥hbar/2=h/4π The diameter of a nucleus is about 10⁻¹⁴ m. If an electron were confined insid... 1
- Predict the effect on the electrical properties of a silicon at room temperature if every millionth silicon atom is replaced by an atom of indium. Given: Concentration of silicon atoms are 5 x 1028 /m3, intrinsic conductivity of silicon is 4.4 x 10-4… Given: N_Si=5×10²⁸ m ⁻³ , σ_i=4.4×10⁻⁴ (Ω m) ⁻¹ , μ_h=0.048 m²/V s. Indium is trivalent, so it acts as an acceptor. Replacing one Si atom in... 1