Week 11 (Geometrical Optics) PHY 098.pptx

Foundation of Physics

1. Geometrical Optics Presented by : ASSOC. PROF. DR. MOHAMAD FARIZ BIN MOHAMAD TAIB 1

2. 2 Units of Week 11: The Law of Refraction Dispersion & Prism The Rainbow Total Internal Reflection Thin Lenses Part 1 (40 minutes) Part 2 (40 minutes) Part 3 (40 minutes) Part 4 (40 minutes)

3. 3 PART 1: THE LAW OF REFRACTION

4. Learning Outcome Part 1: The Law of Refraction At the end of this session, student should be able to :- State the definition of Index of Refraction. Apply the Snell’s Law of refraction; formula (n 1 sin  1 =n 2 sin  2 ). 4

5. 5 INTRODUCTION Geometrical optic Physical optic Used when dealing with the transmission of light in rays. Used when dealing with the inherent nature and properties of light Light is represented as straight lines in a path known as rays Light is represented as a transverse wave front, like the sinusoidal wave It deals with reflection, refraction, total internal reflection and many more. It deals with the phenomenon of interference, diffraction, Young’s double slit experiment and many more

6. 6 Properties of light A form of energy Acts as a form of waves as (part of EM waves) Speed of light, c = 3 × 10 8 ms -1 Travel in straight line (Corpuscular Theory- states that  light  is made up of small discrete particles called " corpuscles " (little particles) which travel in a straight line with a  finite velocity  and possess  impetus . ) Phenomena of light propagation reflection refraction INTRODUCTION

7. 7 This law was discovered in 1621 by the Dutch astronomer and mathematician Willebrord Snell  (also called Snellius). The account of Snell’s law went unpublished until its mention by Christian Huygens in his treatise on light. n 1  and  n 2  represent the indices of refraction for the two media, and α 1  and α 2  are the angles of incidence and refraction that the ray  R  makes with the normal (perpendicular) line  NN  at the boundary. Snell’s law asserts that  n 1 / n 2  = sin α 2 /sin α 1 . History INTRODUCTION

8. Refraction of Light Light moves at different speeds through different media. When it travels from one medium into another, the change in speed causes the ray to bend. 8

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10. 10 where Laws of refraction state : The incident ray, the refracted ray and the normal all lie in the same plane . For two given media, Snell’s law states: OR

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13. 13 Here are some typical indices of refraction:

14. 14 Basic properties of refraction:

15. 15 Refraction can make objects immersed in water appear broken, and can create mirage. Definition mirage: T he deceptive appearance of a distant object or objects caused by the bending of light rays (refraction) in layers of air of varying density

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18. 18 EXAMPLE

19. 19 PART 2 : DISPERSION, PRISMS & THE RAINBOW

20. At the end of this session, student should be able to :- Describe the concept of dispersion. Explain the formation of rainbow. Learning Outcome Part 2: Dispersion, Prism & Rainbow 20

21. Dispersion and Prisms Dispersion is the process of white light splitting into its constituent colours as it passes through a glass prism. A prism is defined as a transparent solid body that has three rectangular lateral surfaces and two triangular faces that are inclined at an angle. 21

22. Copyright © 2010 Pearson Education, Inc. Dispersion and Prisms 22

23. Rainbows are created by the dispersion of light as it refracts in a rain drop. Copyright © 2010 Pearson Education, Inc. The Rainbow 23

24. A ray of light strikes a drop of water in the atmosphere as is refracted and reflected . It first refracted at the front surface of the drop, with the violet light deviating the most and the red light the least . At the back surface of the drop, the light is reflected and returns to the front surface, where it again undergoes refraction. The angle between the incident white light and the returning violet ray is 40  while the angle between the incident white light and the returning red ray is 42  . Basically, the electromagnetic spectrum is made of light with many different wavelengths, and each is reflected at a different angle. Thus, the spectrum is separated, producing a rainbow . The Rainbow 24

25. 25 PART 3 : TOTAL INTERNAL REFLECTION

26. At the end of this session, student should be able to :- Explain the concept of Critical Angle and Total Internal Reflection and its applications e.g. fiber optics; 26 Learning Outcome Part 3: Total Internal Reflection

27. Total Internal Reflection Total internal reflection can occur with 2 condition: when light attempts to move from a medium with high index of refraction to one with a lower index of refraction, and the incident angle is more than critical angle. 27 Critical angle Angle of refraction = 90 o Case 1: θ i < 90 What is critical angle?

28. Applications of total internal reflection An endoscope Binoculars Optical fibre Prismatic periscope 28

29. Copyright © 2010 Pearson Education, Inc. Total Internal Reflection 29

30. 30 A periscope for a submarine uses two totally reflecting 45° - 45°- 90° prisms ( Porro prism) with total internal reflection on the sides adjacent to the 45° angles. It springs a leak, and the bottom prism is covered with water. Explain why the periscope no longer works. ( n w = 1.33, n g = 1.52) Solution :   The 45° angle of incidence for a totally reflecting prism is smaller than the 61° critical angle, so total internal reflection does not occur at the glass-water boundary. Most of the light is transmitted into the water, and very little is reflected back into the prism.   Example :

31. Copyright © 2010 Pearson Education, Inc. 31

32. 32 PART 4 : THIN LENSES

33. At the end of this session, student should be able to :- Identify the focal length of converging and diverging lenses i.e. a converging lens has a positive focal lens 𝑓 = (1/2) 𝑅 and a diverging lens has a negative focal length 𝑓 =(−1/2)R. Draw the Ray Diagrams for Lenses i.e. 3 rays: F-ray, P-ray and C-Ray. State the properties of images produced by converging and diverging lenses i.e. real or virtual image, upright or inverted image, enlarged or reduced in size for image. Identify the position of both object and image either in front of or at the back of the lens. Apply the lens equation 1/ 𝑓 = 1/ p + 1/ q with the correct sign convention for object distance, image distance and focal length (for single lens). Apply the magnification equation. 𝑀 = ℎ ’/ ℎ =− 𝑞 / 𝑝 with the correct sign convention for object distance, image distance, object height, image height and magnification (for single lens). Learning Outcome Part 4 : Thin Lenses 33

34. 1.5 THIN LENSES There are two types of thin lenses. It is converging and diverging lenses. Figures below show the various types of thin lenses, both (a) converging and (b) diverging . (a) Converging (Convex) lenses Biconvex Plano-convex Meniscus Convex (b) Diverging (Concave) lenses Biconcave Plano-concave Meniscus Concave Converging lenses have positive focal lengths and are thickest in the middle Diverging lenses have negative focal lengths and are thickest at the edges 34

35. The sign convention for thin lenses : Physical Quantity Positive sign (+) Negative sign (-) Object distance, u Real object (in front of the refracting surface) Virtual object (at the back of the refracting surface) Image distance, v Real image (opposite side of the object) Virtual image (same side of the object in front of lens) Focal length, f Converging lens Diverging lens Magnification, M Image is upright Image is inverted Using thin lens equations;   35

36. Figure below shows the graphical method of locating an image formed by a converging (convex) and diverging (concave) lenses. Graphical methods for thin lenses F 1 F 2 (a) Converging (convex) lens- same cases with concave mirror 1 1 2 2 O 3 3 I 36

37. 37 Ray 1 - Parallel to the principal axis, after refraction by the lens, passes through the focal point (focus) F 2 of a converging lens or appears to come from the focal point F 2 of a diverging lens. Ray 2 - Passes through the optical centre of the lens is undeviated . Ray 3 - Passes through the focus F 1 of a converging lens or appears to converge towards the focus F 1 of a diverging lens, after refraction by the lens the ray parallel to the principal axis. (b) Diverging (concave) lens - same characteristics with convex mirror O F 2 F 1 1 1 2 2 3 3 I At least any two rays for drawing the ray diagram.

38. Images formed by a diverging lens Figure below shows the graphical method of locating an image formed by a diverging lens. The characteristics of the image formed are ALWAYS virtual upright diminished (smaller than the object) formed in front of the lens . Object position  any position in front of the diverging lens. Front back O F 2 F 1 I 38

39. Object distance, u Ray diagram Image characteristic F 1 F 2 2F 2 2F 1 Images formed by a converging lens depends on the object position Table shows the ray diagrams of locating an image formed by a converging lens for various object distance, u . Front back u > 2 f Real Inverted Diminished Formed between point F 2 and 2F 2 . (at the back of the lens) O 39

40. 40 Object distance, u Ray diagram Image characteristic O F 1 F 2 2F 2 2F 1 u = 2 f Real Inverted Same size Formed at point 2F 2 . (at the back of the lens) Front back f < u < 2 f Real Inverted Magnified Formed at a distance greater than 2 f at the back of the lens. O F 1 F 2 2F 2 2F 1 Front back 40

41. 41 Object distance, u Ray diagram Image characteristic O F 1 F 2 2F 2 2F 1 u = f Real or virtual Formed at infinity. Front back u < f Virtual Upright Magnified Formed in front of the lens. O F 1 F 2 2F 2 2F 1 Front back 41

42. Example An object is placed 25 cm from the converging lens with 15 cm focal length. Find the position of the image and determine whether the image is real or virtual. Solution: Using thin lens equations; The image formed is real ( v is positive value)   42

43. 43 Combination of two (2) or more thin lenses Many useful optical devices require two lenses.   Firstly, the image produced by the first lens is calculated as though the second lens were not present. The light then approaches the second lens as if it had come from the image formed by the first lens. Hence, the image formed by the first lens is treated as the object for the second lens . The image formed by the second lens is the final image of the system. If the image formed by the first lens lies on the back side of the second lens, the image is treated as a virtual object for the second lens, so p is negative. The same procedure can be extended to a system of three or more lenses. The overall magnification of a system of thin lenses is the product of the magnification of the separate lenses. Image 1 = Object 2 Object 1 Image 2

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46. 46 FINAL YEAR QUESTIONS

47. 47 FINAL YEAR QUESTIONS

48. 48 FINAL YEAR QUESTIONS