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Cork Institute of Technology
Bachelor of Engineering (Honours) in Electronic Engineering- Stage 1
(NFQ Level 8)
Autumn 2007
Physics
(Time: 3 Hours)
Instructions Answer FIVE questions
Values for constants: |electron charge | = 1.602 x 10 -19^ C Electron rest mass = 9.110 x 10 –31^ kg Atomic mass unit, u = 1.661 x 10-27^ kg Planck constant = 6.626 x 10 -34^ J s Boltzmann constant = 1.381 x 10 -23^ J K - Speed of light in a vacuum = 2.998 x 10^8 m s- Universal Gravitation constant = 6.673 x 10 -11^ N m^2 kg -
Examiners: Mr. J. A. O’Doherty Dr. S. Foley Prof. G. Hurley
Q1. (a) Explain why interference fringes are formed when thin films are illuminated with monochromatic light. Explain the difference you would expect to see in the visual appearance of the fringes if the source of illumination was white light? (10 marks) (b) When a plane wave of light is shone through a diffraction grating, the second order spectrum line appears at an angle of 19.123°. Calculate the number of grooves per millimetre in the grating, if the wavelength of the light is 546 nm. Also, estimate the maximum number of visible orders. (10 marks)
Q2. (a) Light with a wavelength 633 nm is incident on the core of an optical fibre that has refractive index1.46. What are the wavelength, frequency and speed of the light in the core? (8 marks) (b) Calculate the focal length of a glass plano-convex lens, if the radius of curvature of the concave surface is 400 mm. The refractive index of the glass is 1.48. (6 marks) (c) Calculate the maximum and minimum magnifying powers for a single-lens magnifier that has a focal length of 8.06 mm. Explain where the final image is located for each case. (6 marks)
Q3. (a) The equation for the displacement of a one dimensional progressive electromagnetic
wave in a solid is; y = 1.5 x 10-9 cos(1.5708 x 10^6 x - 1.3464 x 10^14 t ) , where all quantities are in S I units. Calculate values for the amplitude, frequency, wavelength and velocity of the wave. Also, calculate the refractive index of the material. (12 marks) (b) Calculate the maximum viewing distance for a pair of binoculars, in order to distinguish clearly the lettering on a distant sign, if the smallest detail in the letters is 2 mm in size. Assume that the wavelength of day-light (average) is 500 nm and the diameter of the objective lens in the binoculars is 50 mm. (8 marks)
Q4. (a) Prove that the period T of a spring system of mass m , which oscillates in simple harmonic
motion, is given by the equation; T = 2 π mk , where k represents the elastic constant of
the spring. (12 marks) (b) The reference power level used in telecommunications is 1 mW. Calculate the power in mW of a signal in a communications channel that has a level of -25 dB ( minus 25 dB ) with respect this reference. (8 marks)
Q5 (a) (i) Calculate the kinetic energy of a uniform solid disc that is rotating at 1200 rpm about a fixed axis of rotation. The disc has a mass of 20 kg and diameter of 250 mm. (ii) If the disc is slowed down and stopped in 15 seconds by a braking system, what is the torque generated by the brakes, assuming the deceleration is constant? (12 marks) (b) A spring system, which is oscillating in simple harmonic motion, has a mass of 0.5 kg, energy of 174.4 mJ and amplitude of 80 mm. Calculate the period of the system. (8 marks)
Q6. (a) Prove that the number of nuclei (Nt ) in a sample which survive radioactive decay is given
by the equation; (^) N (^) t = No e-^ λ^ t, where (λ) and (No ) represents the radioactive decay constant and the initial number of nuclei in the sample respectively. (10 marks) (b) Explain the principle of operation of radioactive carbon dating. Calculate the elapsed time before the activity of carbon-14 in an archaeological artefact has declined to 170 Bq kg -1^. The corresponding activity of a living specimen is 250 Bq kg-1^. Half-life of the carbon-14 isotope is 5730 years. (10 marks)
Useful Equations
Simple harmonic motion; v = ±ω(r 2 – s 2 ) 1/2^ a = -ω^2 s Period, (T); oscillating spring system; T = 2π(m/k) 1/2^ ; orbit;T = 2π[R^3 /(G M)]1/
Rotation; kinetic energy = ½ I ω^2 torque (τ) = (I) x (α)
power = (τ) x (ω) I (^) disc = M R^2 /2, I (^) sphere = 0.4 M R^2 Thermal expansion; α = (∆L/L)(∆θ) - Young’s modulus of elasticity; E = (tensile stress)/(tensile strain)
Wave equation; (^) y = a cos[ (^2) λ^ π(x - v t)]
Doppler: detector moving towards a transmitter; ∆f/f = v (^) R/v Speed of a wave on a stretched string; v = (1/2L)(T/m)1/ Refractive index, n =c/v Lens makers formula; 1/f = (n – 1)(1/R 1 –1/R 2 )
Optical fibre; numerical aperture, N A = n (^) o sinαmax = √(n 12 – n 22 ) Resolution of a microscope; d = 1.22 λ/(2 n sinα) = 1.22 λ/(2 N A)
Thickness of an interference wedge; T = 2 xL λ
Thickness of an antireflection coating, T = 4 n^ λo
Diffraction in a single slit:
- the position of the minima is given by; sinθ = m λ/w
- the position of the missing fringes mm = d/w Brewster angle, (θ (^) B); for plane polarized reflected light; tanθB = n (^) 2/ n 1
Radiated energy; Stephan-Boltzmann law; W = ε σ T^4
Wien displacement law; λmax T = constant
Photoelectric equation; (1/2)mv (^2) max = hf - φ
deBroglie equation λ = h/p ‘Uncertainty Principle’ equation; (^) ∆p (^) ∆x (^) ≥ h/4π
Number of surviving radioactive nuclei; (Nt ) = N (^) o exp(-λ t)
Half life; T (^) 1/2 = 0.693/λ Einstein equation; E = m c 2 ; Conversion factor; 1 u = 931.5 MeV Gain of a PM tube; G = ηn
