Applied Physics
- Determine the curl of these vector fields. (1) \(\vec A=\hat a_x(2x^2+y^2)+\hat a_y(xy-y^2)\) (2) \(\vec A=yz\,\hat a_x+4xy\,\hat a_y+y\,\hat a_z\) nabla×vec A=beginvmatrixhat a_x&hat a_y&hat a_z\\ ∂_x&∂_y&∂_z\\ A_x&A_y&A_zendvmatrix (1) A_x=2x²+y² , A_y=xy-y² , A_z=0 x-component: ∂_yA_z... 1
- Define the terms: Critical angle, Acceptance angle and Attenuation. Critical angle ( θ_c ): The angle of incidence in the denser medium (the core) at the core–cladding interface for which the angle of refract... 1
- Derive an expression for numerical aperture of a step index optical fibre. Give its physical significance. 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
- What is antireflection coating? What should be the refractive index and minimum thickness of the coating? Antireflection (AR) coating: A thin transparent film, for example MgF₂, deposited on a lens or glass surface. Light reflected from its upper... 1
- In Newton’s rings experiment the diameter of 5th ring was 0.336 cm and the diameter of 15th ring was 0.590 cm. Find the radius of curvature of plano convex lens if the wavelength of light used is 5890 Å. Given: D₅=0.336 cm, D₁₅=0.590 cm, so p = 10. λ=5890 Å =5.89×10⁻⁷ m. Air film (μ = 1). Formula: D_(n+p)²-D_n²=4pλ R⇒ R=dfracD_(n+p)²-D_n²4pλ... 1
- What is resonant cavity? Explain its use in the generation of Laser beams. Resonant cavity (optical resonator): A pair of mirrors placed facing each other, parallel (or confocal), at the two ends of the active mediu... 1
- Explain the de Broglie hypothesis of mater waves. de Broglie hypothesis (1924): Radiation has a dual nature: waves (interference) and particles (photoelectric effect). Nature loves symmetry,... 1
- Derive Schrodinger’s Time Independent wave equation for matter waves. The wave associated with a particle moving along x can be written as psi(x,t)=A e^(i(kx-ω t))=psi₀(x) e^(-iω t) where psi₀(x)=Ae^ikx . Diffe... 1
- Define drift velocity and Mobility. Write its unit. Drift velocity ( v_d ): When an electric field is applied to a conductor or semiconductor, the free charge carriers acquire a small average... 1
- The ground state energy of an electron in an infinite well is 1 eV. What will be the ground state energy if the width of the well is doubled? Formula: E_n=n²h²/8mL² , so for the ground state E₁∝1/L² . E₁'/E₁=Big(L/L'Big)²=Big(L/2LBig)²=1/4 E₁'=1/4×1\ eV New ground-state energy = 0.... 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
- What do you mean Curl of vector. Write its significance. Curl: The curl of a vector field vec A is a vector whose magnitude is the maximum circulation of vec A per unit area, as the area shrinks to... 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
- 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
- An optical fiber of core refractive index of 1.50 is to be clad to ensure that TIR will take place for a light ray with critical angle 85°. What minimum refractive index is allowed for cladding? Given: n₁=1.50 , θ_c=85^° . Formula: sinθ_c=n₂/n₁⇒ n₂=n₁sinθ_c n₂=1.50×sin85^°=1.50×0.9962=1.494 Refractive index of cladding n₂≈1.494 This... 1
- 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
- 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
- Find the minimum thickness of soap film which appears dark (Wavelength [first digit partly illegible in the source scan; read as 5]896 A°) in reflection when light is incident normally on the film. Given refractive index of the film is 1.33. Assumption: The first digit of the wavelength is obscured in the scan. We take λ=5896 Å (the sodium D-line). Given: λ=5.896×10⁻⁷ m, μ=1.33 ,... 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
- 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
- Explain optical resonator in LASER? Optical resonator is the arrangement of two mirrors placed at the ends of the laser's active medium, facing each other and aligned with its... 1
- List and briefly explain any two industrial applications of laser. Lasers produce a highly directional, monochromatic, coherent and very intense beam that can be focused to a tiny spot (about µm) with power... 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