20 16 A student carried out an experiment to determine the focal length of a converging lens. The student used a bulb to illuminate an object as shown. The converging lens produced an image of the object on a screen. The student adjusted the position of the screen until the image was in focus. He repeated the procedure for different distances between the object and the lens. The distance v from the lens to the screen was measured for each lens position. bulb object lens screen v The student measured the height ho of the object and the height hi of the corresponding image on the screen for each lens position. The magnification m was calculated. To determine the focal length f of the lens the student used the equation m v f = −1 (a) Explain why a graph of m on the y-axis and v on the x-axis should be a straight line. (2) .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. (b) The student obtained the following data. object height, ho = 2.04 cm v / cm hi / cm m 61.5 5.92 2.90 47.0 4.24 2.08 39.6 3.30 1.62 31.2 2.15 23.8 1.33 0.652 (i) Complete the table and plot a graph of m against v on the grid opposite. (6) Turn over 21 22 (ii) Determine a value for f. (3) .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. f = ...................................................... (c) If the distance from object to the lens is less than a certain value, no image is produced on the screen. Explain why. (3) .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. (Total for Question 16 = 14 marks) TOTAL FOR SECTION B = 26 MARKS TOTAL FOR PAPER = 80 MARKS Turn over 23 List of data, formulae and relationships Acceleration of free fall g = 9.81 m s–2 (close to Earth’s surface) Electron charge e = –1.60 × 10–19C Electron mass me = 9.11 × 10–31kg Electronvolt 1 eV = 1.60 × 10–19J Gravitational field strength g = 9.81 N kg–1 (close to Earth’s surface) Planck constant h = 6.63 × 10–34J s Speed of light in a vacuum c = 3.00 × 108m s–1 Mechanics Electric circuits Potential difference V W Q = Resistance R V I = Electrical power and energy P = VI P = I 2R P V R = 2 W = VIt Resistivity ρl R A = Current I Q t = ∆ ∆ I = nqvA Kinematic equations of motion s u v t = + ( ) 2 v = u + at s = ut + at2 v2 = u2 + 2as Forces ΣF = ma g F m = W = mg moment of force = Fx Momentum p = mv Work, energy and power ΔW = FΔs Ek = mv2 ΔEgrav = mgΔh P E t = P W t = efficiency = useful energy output total energy input efficiency = useful power output total power input 1 2 1 2 24 Materials Waves and Particle Nature of Light Wave speed v = fλ Speed of a transverse wave on a string T v μ = Intensity of radiation I P A = Power of a lens P f = 1 P = P1 + P2 + P3 + … Thin lens equation 1 u + = 1 1 v f Magnification for a lens m v u = = image height object height Diffraction grating nλ = d sin θ Refractive index n1 sin θ1 = n2 sin θ2 n c v = Critical angle sin C n = 1 Photon model E = hf Einstein’s photoelectric equation hf = ϕ + ½mv 2 max de Broglie wavelength λ = h p Density m ρ V = Stokes’ law F = 6πηrv Hooke’s law F = kΔx Pressure p F A = Young modulus Stress F σ A = Δ Strain x ε x = σ E ε = Elastic strain energy ΔEel FΔx 1 2 =