Lectures 21-22 OPTICS The law of reflection The law of refraction

1. Lectures 21-22 OPTICS The law of reflection The law of refraction

2. Light as electromagnetic wave Light is an electromagnetic wave, a transverse wave that travels through empty space at the speed of 3*10E+8 m/s or 186000miles/s. Visible light wavelength A wave front is a line connecting points all having the same phase of vibration. Far away from the source of light the circular front look more like plane fronts. The waves are then called plane waves. A line drawn perpendicular to the wave front is called a ray of light and represents the direction of propagation of the light wave.

3. OPTICS, the study of light • Geometrical optics(the light rays are dealt with in the analysis of an optical system) • Wave optics or physical optics (analysis of an optical system is done in terms of waves) • Quantum optics (treating light as little bundles of electromagnetic energy called photons)

4. Huygens` principle Huygens principle states that each point on a wave front may be considered as a source of secondary spherical wavelets. These secondary wavelets propagate in the forward direction at the same speed as the initial wave. The new position of the wave front at a later time is found by a drawing the tangent to all of these secondary wavelets at the later time.

5. The law of reflection In triangle B1EO

6. The law of reflection The first law of reflection says that the angle of incidence i is equal to the angle of reflection r. the second law of reflection was implied in the derivation and it says that the incident ray, the normal, and the reflected ray all lie in the same plane

7. The plane mirror p is the object distance q is the image distance Real image is one on which all the rays are converging Virtual image is one from which all the rays are diverging From triangle OSA From triangle SIA The image is as far behind the mirror as the object is in front of it

8. Optical image characteristics • Its nature (real or virtual) • Its orientation (erect, inverted, perverted) • Its size (enlarged, true, or reduced) For example, a plane mirror produces a virtual, perverted, true image

9. Example. An image in a plane mirror. If a object 15.0cm high is placed 20.0cm in front of a plane mirror, where is the image located and how high is the image? For a plane mirror, the height of the image is equal to the height of the object

10. The concave spherical mirror A spherical mirror is a reflecting surface, whose radius of curvature is the radius of the sphere from which the mirror is formed. The principal axis or optical axis is the line going through the center of the mirror. Light rays that are parallel and close to the principal axis of the concave mirror converge to a point called the principal focus F of the mirror. The principle of reversibility: if a ray traces a certain path through an optical system in one direction, then a ray sent backward through the system along the same path, traverses the original path and comes out along the line that the original ray entered

11. The concave spherical mirror Focal length of a concave spherical mirror The focal length of a spherical mirror is equal to one-half the radius of curvature of the mirror

12. The concave spherical mirror Location of an image by ray diagram • Ray (1), in red, is drawn parallel to the principal axis. On striking the mirror, it is reflected through the principal focus F. • Ray (2), in green, is drawn through the principal focus F. On striking the mirror, it is reflected parallel axis because all rays that emanate from principal focus come out parallel to the principal axis after reflection • Ray (3), in blue, is drawn through the center of curvature C. it is reflected upon itself, since it lies along the normal

13. The concave spherical mirror The mirror equation The mirror equation The mirror equation shows the relation between the focal length f of the mirror, the object distance p, and the image distance q.

14. The concave spherical mirror Magnification The linear magnification M The magnification tells how much larger the image is than the object If M is negative the image is inverted The possible cases of magnification:

15. The convex spherical mirror: Some special cases Case 1: the object is located at infinity Case 2: the object is at the center of curvature

16. The convex spherical mirror: Some special cases Case3: the object is located between the center of curvature and the principal focus Case 5: the object lies within the principal focus Case 4: the object is at principal focus Virtual enlarged erect image

17. Example. An object is placed within the principal focusof a concave spherical mirror. An object, 5.00 cm high, is placed 7.00 cm in front of a concave spherical mirror of 10.00-cm focal length. Find the location of its image and its final size.

18. The convex spherical mirror Radius and focus length are negative

19. The convex spherical mirror Location of an image by a ray diagram • The first Ray (1), in red, is drawn parallel to the principal axis and it is reflected from the mirror as if it came from the principal focus F. • Ray (2), in green, is drawn straight toward the principal focus F. It is reflected parallel to the principal axis before it can get to the principal focus. • Ray (3), in blue, is drawn through the center of curvature C. it is reflected upon itself, since it lies along the normal The image of a real object is always erect, virtual and reduced

20. Sign conventions for spherical mirrors

21. Example. Convex spherical mirror. An object, 5.00 cm high, is placed 30.0 cm in front of a convex spherical mirror of -10.00-cm focal length. Find the location of its image and its final size.

23. The law of refraction The bending of light as it passes from one medium into another is called refraction

24. The law of refraction The law of refraction The ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the speed of light in medium 1 to the speed of light in medium 2. wavelength If medium 1 is vacuum frequency n is the index of refraction Snell`s law

25. The law of refraction

26. The law of refraction Whenever a ray of light goes from a rarer medium to a denser medium the refracted ray is always bent toward the normal Whenever a ray of light goes from a denser medium to a rarer medium the refracted ray is bent away from the normal

27. Apparent depth of an object immersed in water

28. Refraction through parallel faces

29. Total internal reflection The angle of incidence that causes the refracted ray to bend through 90 is called the critical angle of incidence. When the incident angle becomes greater than the critical angle, no refraction occurs. That is, no light enters the second medium at all; all the light is reflected. This condition is called total internal reflection, because refraction has been eliminated entirely.

30. Total internal reflection This ordinary piece of glass (the critical angle of 41.8), cut into the shape of a triangle, with an angle greater than the critical angle is called a prism

31. Dispersion The separation of white light into its component colors is called dispersion. The band of colors is known as a spectrum Dispersion occurs because the index of refraction is not strictly a constant for a particular material, but rather varies slightly with wavelength. For example, n for red light (700nm) is 1.51, for violet (400nm) is 1.53

32. Thin lenses An optical lens is a piece of transparent material, such as glass or plastic The net effect of the two refractions is to take a ray of light, which is parallel to the principal axis, and bend it such that it crosses the principal axis. The point where this ray crosses the principal axis is called the principal focus, and is designated by the letter F.

33. Thin lenses The equation that relates the focal length, index of refraction, and radii of curvature of a lens is called the lensmaker`s formula. We assume that the thickness of the glass lens is negligible compared to the distance to the principle focus and to any object or image distance concerned. Such a lens of negligible thickness is called a thin lens. (R1>0, R2<0)

34. A converging lens All rays parallel and close to the principal axis converge to the principal focus. Examples of converging lenses A converging lens is always thicker at the center of the lens than it is at the rim

35. A diverging lens All rays parallel and close to the principal axis diverge from the principal focus. Examples of diverging lenses A converging lens is always thinner at the center of the lens than it is at the rim

36. The lens equation In triangle OPC In triangle QIC In triangle ACF In triangle IQF The lens equation

37. Some special cases for the convex lens Case1: the object is located at infinity Case 2: the object lies between infinity and 2f, that is, The object moves toward the lens the image moves away from the lens and gets bigger

38. Case 3: the object is located at a distance of twice the focal length from the lens, that is Case 4: the object is located between the focal length and twice the focal length from the lens, that is

39. Case 5: the object is located at the principal focus of the lens, that is p=f Case 6: the object is placed within the principal focus of the lens, that is p<f When a convex lens is used with the object located within the principal focus it is called a simple magnifying glass. In this case, the image q is always negative

40. In summary, for a converging lens with the object distance p positive If the image distance q is positive the image is real and located on the other side of the lens. If the image distance is negative, the image is on the same side of the lens as the object and is a virtual image