Chapter 12

1. Chapter 12 Physics Beyond 2000 Optical Instruments

2. Geometric Optics • In this chapter, the lenses and mirrors have dimension much longer than the wavelength of light. • Effect of diffraction can be ignored. • Light is regarded as ray. http://webphysics.davidson.edu/physletprob/ch18_v4_physlets/optics4/default.html http://www.phy.ntnu.edu.tw/demolab/index.html

3. Reflection • Laws of reflection. http://www.netzmedien.de/software/download/java/brechung/

4. Plane mirror • What are the properties of the image? http://www.continental.clara.net/physics/lt31.htm Note that we cannot capture a virtual image on a screen.

5. search pin plane mirror image object Locate a virtual image • Method of no parallax Use a long search pin to locate the image behind the mirror. In front of the mirror, view the image in the mirror and the search pin.

6. search pin image in the mirror eye eye Locate a virtual image • Method of no parallax If the search pin is at the exact position of the image, the image in the mirror and the search pin always coincide even if we change the angle of view.

7. search pin I O real image Locate a real image • The method of no parallax can be applied to locate the position of real images.

8. Normal 2 Normal 1 Reflected ray 1 Fixed incident ray θ Reflected ray 2 2θ Mirror 1 Mirror 2 Rotation of a plane mirror Rotate the plane mirror from position 1 to position 2 by an angle θ. The reflected ray will turn through 2θ.

9. Rotating a plane mirror • Light-beam galvanometer.

10. position 2 position 1 image 1 image 2 fixed object 2v v A moving mirror If the plane mirror moves at a speed v, the image moves at speed 2v.

11. Concave mirrors • http://www.fed.cuhk.edu.hk/sci_lab/ntnujava/Lens/lens_e.html

12. Spherical aberration • If the aperture of the mirror is large, the reflected rays do not all passes through the focus. • This is called spherical aberration.

13. Spherical aberration • It can be corrected by using a parabolic mirror.

14. paraxial ray θ θ h 2θ θ C F r f Focal length f and radius of curvature R Show that r = 2f for small angles.

15. Images for concave mirror http://www.fed.cuhk.edu.hk/sci_lab/ntnujava/Lens/lens_e.html

16. f θ θ F C h Example 1 • The rays from the sun are parallel and the image of the sun is on the focal plane.

17. θ θ h α γ β O C F I r u v Mirror formula for small angles

18. for small angles Mirror formula Real-is-positive convention:

19. for small angles Mirror formula Real-is-positive convention:

20. I O C F u v Linear magnification m

21. Example 2 • Justify the nature of the image from the sign of image distance v.

22. Variation of image with object distance http://www.fed.cuhk.edu.hk/sci_lab/ntnujava/Lens/lens_e.html

23. Variation of magnification with object distance

24. for small angles Convex mirror

25. Convex mirror http://www.fed.cuhk.edu.hk/sci_lab/ntnujava/Lens/lens_e.html http://www.iln.net/html_p/c/453262/453270/453373/454123/56652_2079292.asp

26. O I F I u v Example 3

27. θ θ F C h Measure the focal length of concave mirror Method A • Object at infinity. • Image is at the focal plane. • Measure the distance between the mirror and the screen. f

28. Measure the focal length of concave mirror Method B • Object at the radius of curvature. • Image is at the radius of curvature. • Use the method of no parallax to locate the image. • Adjust the position of the object so that its image is • coincide with the object. • Measure the distance between the object and the mirror. http://www.usafa.af.mil/dfp/physics/webphysics/Physlet_examples/concave_mirror_f.html

29. Measure the focal length of concave mirror Method C • Object at different positions to produce real images. • Images are captured by a screen. 0

30. Measure the focal length of concave mirror Method D • Object at different positions to produce real images. • Images are captured by a screen. • Calculate the linear magnification m. m slope = 0 v -1

31. O P Q C I mirror lens Measure the focal length fmof a convex mirror • It is not possible to capture a virtual image on a screen. • Put a converging lens of focal length flens in front of the convex mirror. • Adjust the position of the object so that a real image is at the same position as the object. s 2.fm flens

32. O P Q C I mirror lens Measure the focal length fmof a convex mirror • Measure s, the separation between the lens and the convex lens. • 2  focal length of the convex mirror is flens – s. s 2.fm flens

33. Medium 1: 1, 1, c1 and n1 1 2 Medium 2: 2, 2, c2 and n2 Refraction http://www.fed.cuhk.edu.hk/sci_lab/download/project/Lightrefraction/LightRefract.html http://www.netzmedien.de/software/download/java/brechung/

34. Medium 1: 1, 1, c1 and n1 1 2 Medium 2: 2, 2, c2 and n2 Refraction Snell’s law: n1.sin1 = n2.sin2

35. Medium 1: 1, 1, c1 and n1 1 2 Medium 2: 2, 2, c2 and n2 Refraction If n2 > n1, then medium 2 is an optically denser medium and medium 1 is an optically less dense medium

36. refraction with 1 < c. medium 1 critical case with 2 = c. medium 2 2 3 1 total internal reflection with 3 > c. Total internal reflection This occurs when light travels from an optically denser medium to an optically less dense medium and the angle of incidence > critical angle c. http://www.fed.cuhk.edu.hk/sci_lab/ntnujava/light/flashLight.html

37. The critical angle c is given by refraction with 1 < c. medium 1 of n1 critical case with 2 = c. medium 2 of n2 2 3 1 total internal reflection with 3 > c. Total internal reflection http://www.continental.clara.net/physics/lt23.htm

38. Fish-eye view • http://www.fed.cuhk.edu.hk/sci_lab/ntnujava/fishEye/fishEye.html

39. Example 4 • The critical angle of glass with n = 1.5 is about 42o in air. • It depends also on the medium in which the glass is immersed.

40. 45o 45o 45o 45o Reflecting prism • Angle of incidence = 45o > Critical angle = 42o. • Total internal reflection occurs inside the glass prism. • The glass prism can be used as a reflecting mirror.

41. Optical fibre • There is total internal reflection inside the optical fibre. • Light is guided to travel in the optical fibre.

42. air B C apparent depth medium with refractive index n I real depth O Real depth and apparent depth • The image I is displaced upwards relative to the object O.

43. for small angles. air B C apparent depth medium with refractive index n I real depth O Real depth and apparent depth

44. I O B C Real depth and apparent depth Where would be the image if we are inside the medium? Suppose that the angles are small. air medium with refractive index n

45. Measure the refractive index of glass Find the real depth and apparent depth from h1 and h2. eye travelling microscope h2 h1 h h h glass block O2 I O1 O1 real depth = h2 apparent depth = h2 – h2

46. w i r r i d Rectangular glass block The incident ray and the emergent ray are parallel. The lateral displacement is incident ray emergent ray

47. A D 2 2 1 1 Prism Find the angle of deviation D in terms of angles of incidence (1and 2) and angles of refraction (1 and 2). D = (1 - 1)+(2 - 2)

48. A D 2 2 1 1 Prism Find the refracting angle A of the prism in terms of the angles of incidence and angles of refraction. A = 1+ 2

49. A D 2 2 1 1 Prism The angle of deviation is a minimum Dmin when the light ray is symmetrical. Find the refractive index n of the glass prism.

50. A D Small-angled prism • For a prism with small refracting angle A. • The angle of deviation D = (n - 1).A • The angle of deviation is independent of the angle of incidence.