#mu engineering
- State Ampere’s Circuital law. Derive Maxwell’s fourth equation in differential form. Ampere's circuital law: The line integral of the magnetic field intensity vec H around any closed path equals the net current enclosed by th... 1
- With a neat energy level diagram, describe the 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 are the characteristics of good fuel? A good fuel should: Have a high calorific value, so it gives more heat per unit mass. Have a moderate ignition temperature. If it is too low... 1
- Define corrosion, how you will join the metals to prevent corrosion, justify with diagram. Corrosion is the gradual destruction or deterioration of a metal by chemical or electrochemical attack from its environment, starting at the... 1
- Give the purposes of making of an alloy. Alloys are made in order to: Increase hardness and strength. Pure metals are soft. Example: adding C to Fe gives steel; adding Cu to Au make... 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
- 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
- Show that the divergence of the 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
- Calculate the wavelength of de-Broglie waves associated with mass 1 kg moving with a speed of 103 m/sec. Given: m=1 kg, v=10³ m/s, h=6.63×10⁻³⁴ J s. Formula: λ=h/mv λ=frac6.63×10⁻³⁴1×10³=6.63×10⁻³⁷\ m λ=6.63×10⁻³⁷ m This is far too small to dete... 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
- Write Fermi- Dirac distribution function and explain the terms 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- Write 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
- 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
- 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
- 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