Wave Optics

Wave Optics explains the phenomena that ray optics cannot, such as the bright and dark bands formed when light passes through narrow slits, by treating light as a wave. In this chapter you will learn Huygens' principle, in which every point on a wavefront acts as a source of secondary wavelets, and use it to derive the laws of reflection and refraction and show that light travels more slowly in a denser medium. You will learn the meaning of coherent sources and why two independent bulbs cannot produce a steady interference pattern. You will study Young's double slit experiment, the conditions for constructive and destructive interference, and derive the fringe width, beta = lambda D/d. The chapter explains diffraction of light at a single slit, the angular width of the central maximum and how diffraction differs from interference. Finally, you will learn that polarisation proves light is a transverse wave, and study polaroids, Malus' law, polarisation by scattering and Brewster's law for polarisation by reflection.

Detailed Worksheet: Wave Optics Section A - Definitions (10 marks) 1. State Huygens' principle. What is a wavefront? (2 marks) 2. What are coherent sources? Why are they necessary for a sustained interference pattern? (2 marks) 3. Write the conditions for constructive and destructive interference in terms of path difference. (2 marks) 4. State Malus' law. (2 marks) 5. State Brewster's law. Write the relation between Brewster's angle and refractive index. (2 marks) Section B - Calculations and Applications (15 marks) 6. In a double slit experiment, the slits are 0.28 mm apart and the screen is 1.4 m away. The distance between the central bright fringe and the fourth bright fringe is 1.2 cm. Find the wavelength of light used. (3 marks) 7. In Young's experiment, light of wavelength 600 nm is used with slit separation 1 mm and screen distance 1 m. Find the fringe width and the distance of the third dark fringe from the central maximum. (3 marks) 8. Light of wavelength 500 nm falls on a single slit of width 0.2 mm, and the pattern is observed on a screen 1 m away. Find the angular position of the first minimum and the width of the central maximum. (3 marks) 9. Light of wavelength 589 nm in air enters water (n = 1.33). Find its speed, wavelength and frequency in water. (3 marks) 10. Unpolarised light of intensity I0 passes through a polariser and then an analyser whose axis is at 60 degrees to the polariser. Find the intensity of the light emerging (i) from the polariser and (ii) from the analyser. Also find Brewster's angle for glass of refractive index 1.5. (3 marks) Section C - Diagrams (10 marks) 11. Draw a diagram showing refraction of a plane wavefront at a plane surface using Huygens' construction, and use it to derive Snell's law. (4 marks) 12. Draw a labelled diagram of Young's double slit experiment and the intensity distribution of the fringes on the screen. (3 marks) 13. Draw the intensity distribution of the diffraction pattern due to a single slit, marking the central maximum and the first minima on both sides. (3 marks) Section D - Analysis and Higher-order Thinking (15 marks) 14. A beam of light containing wavelengths 650 nm and 520 nm is used in Young's experiment with slit separation 2 mm and screen distance 1.2 m. Find (i) the distance of the third bright fringe of 650 nm from the central maximum and (ii) the least distance from the central maximum where bright fringes of both wavelengths coincide. (5 marks) 15. Compare interference and diffraction patterns on four bases. Explain what happens to the fringe width in Young's experiment when (i) the whole apparatus is immersed in water, (ii) the slit separation is doubled and (iii) red light is replaced by blue light. (5 marks) 16. Explain why polarisation shows that light is a transverse wave. Explain how light is polarised by scattering and by reflection, and derive Brewster's law tan iB = n. Give two uses of polaroids. (5 marks) Instructions: Time allowed 2 hours. Attempt all sections. Convert all lengths to SI units and draw neat, labelled diagrams.