14   17 A simple astronomical refracting telescope consists of two converging lenses. Light from a star is brought to a focus by the objective lens and then viewed through an eyepiece lens as shown. objective lens eyepiece lens light from a star (a) (i) In the arrangement shown, the final image is formed at infinity. Explain why the separation of the objective and eyepiece lenses is equal to the sum of their focal lengths. 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(ii) State why the final image is inverted. (1) .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. Turn over 15   (b) Glass lenses used for optical instruments often have an anti-reflective coating. The coating is a thin layer of a transparent substance with refractive index nc. Light is reflected from the coating surface and from the lens surface as shown. The reflected light interferes destructively. light reflected from lens light reflected from coating coating lens When a single-layer coating is used, the coating thickness is chosen to eliminate reflections for green light, which is in the middle of the visible spectrum. (i) Calculate the minimum thickness d of the coating required for the reflection of green light to be eliminated. frequency of green light = 6.00 × 1014 Hz nc = 1.38 (4) .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. d = ...................................................... 16   (ii) State why white light reflected from coated lenses is seen as purple. (1) .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. (Total for Question 17 = 8 marks) Turn over 17   18 The harp is a musical instrument with many strings, as shown. (Source: © Peter Voronov/Shutterstock) All the strings are under tension. The strings on one type of harp are made from nylon of density 1070 kg m−3. One string has a diameter of 1.14 mm. (a) (i) Show that the mass per unit length μ of the string is about 1.1 × 10−3 kg m−1. (2) .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. 18   (ii) When the middle of the string is plucked, a note of frequency 440 Hz is produced. Calculate the tension in the string. length of string = 41.0 cm (4) .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. Tension in string = ...................................................... Turn over 19   (b) The graph shows how the Young modulus E of the nylon varies with temperature. 0 30 25 20 15 10 5 Temperature / °C E When the harp is played, the temperature of the string increases. Explain how this temperature change would affect the frequency of the note produced when the string is plucked. 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(Total for Question 18 = 9 marks)