Thin Lenses. Lecture 25. Chapter 23. Ray Optics. Physics II. Course website:

Transcription

1 Lecture 25 Chapter 23 Physics II Ray Optics Thin Lenses Course website: Lecture Capture:

2 Total internal reflection (leftovers)

3 ConcepTest A laser beam passing from medium 1 to medium 2 is refracted as shown. Which is true? Refraction A. n 1 < n 2. B. n 1 > n 2. C. There s not enough information to compare n 1 and n 2. n 2 < n 1 It bends away from the normal

4 n 2 < n 1 angle of incidence Total Internal Reflection Normal angle of refraction Refracted ray air =900 n glass 1 < Incident ray Reflected ray When a ray crosses a boundary into a material with a lower index of refraction, it bends away from the normal. As the angle 1 increases, the refraction angle 2 approaches 90, and the fraction of the light energy transmitted decreases while the fraction reflected increases. The critical angle of incidence occurs when 2 = 90 : The refracted light vanishes at the critical angle and the reflection becomes 100% for any angle 1 > c.

5 Critical angle (TIR) n 2 < n 1 n 1 Normal angle of refraction air =90 0 glass Refracted ray =90 0 Critical angle (incident angle) Angle of refraction, so 1 sin sin 90 Total Internal Reflection Critical angle sin

6 Fiber Optics The most important modern application of total internal reflection (TIR) is optical fibers. Light rays enter the glass fiber, then impinge on the inside wall of the glass at an angle above the critical angle, so they undergo TIR and remain inside the glass. The light continues to bounce its way down the tube as if it were inside a pipe.

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8 Lenses

9 There are two types of lenses A converging lens causes the rays to refract toward the optical axis. A diverging lens refracts parallel rays away from the optical axis A converging lens is thicker in the center than at the edges. A diverging lens is thicker at the edges than in the center.

10 Lensmaker s Equation This useful equation relates the radii of curvature of the two lens surfaces, and the index of refraction, to the focal length:

11 Converging Lens

12 There are three typical situations which are used in Ray Tracing for a converging lens: A ray initially parallel to the optic axis will go through the far focal point after passing through the lens. A ray through the near focal point of a thin lens becomes parallel to the optic axis after passing through the lens. A ray through the center of a thin lens is neither bent nor displaced but travels in a straight line. Ray 1 Ray 2 Ray 3

13 Converging lens. Real Image Object P Object plane R h Optical axis 2 3 Near focal point 1 F 1 Lens plane O S Object distance S f f (focal length) F 2 Far focal point Image distance R h' P Image plane Image (inverted real image) Note!!! For a converging lens f is positive f > 0 and S > 0 is positive all the time s> 0 If after using the lens equation, s is positive If after using the lens equation, s is negative Image is real Image is virtual Demo: cat/flashlight/screen/lens To demonstrate how to test a real image

14 Examples of real inverted images

15 ConcepTest A lens produces a sharply focused, inverted image on a screen. What will you see on the screen if a piece of dark paper is lowered to cover the top half of the lens? top half of the lens? Half-blocked lens. A. An inverted but blurry image. B. An image that is dimmer but otherwise unchanged. C. Only the top half of the image. D. Only the bottom half of the image. E. No image at all. 1 screen 2 3 O F 2 F 1 Still the same image but it is created by less number of rays Image (inverted image)

16 Magnification The image can be either larger or smaller than the object, depending on the location and focal length of the lens. (inverted image) Δ Δ The lateral magnification m is defined as: The minus is introduced so that: A positive value of m indicates that the image is upright relative to the object. A negative value of m indicates that the image is inverted relative to the object. End of the class

17 Converging lens. Virtual Image Consider a converging lens for which the object is inside the focal point, at distance s < f. Image (virtual image in upright position) h' 1 3 F h O 2 Optical axis F Object 1 S Object distance Image distance 2 S The image distance S ' for a virtual image is defined to be a negative number S ' <0). For a converging lens f > 0 After using the lens equation, s must be negative Image is virtual You can see all three rays appear to diverge from point P. Image is an upright and virtual. f

18 You can see a virtual image by looking through the lens. This is exactly what you do with a magnifying glass, microscope or binoculars. Virtual Magnified Images Doc uses a magnifying glass in 1955 to read the letter written by his 1985 counterpart. Slide

19 ConcepTest A lens creates an image as shown. In this situation, the object distance s is Converging lens A. Larger than the focal length f. B. Equal to the focal length f. C. Smaller than focal length f. s > f The image is inverted and real. It is only possible when s > f s < f

20 Diverging Lens

21 There are three typical situations which are used in Ray Tracing for a diverging lens: Ray 1 Ray 3 Ray 2

22 Consider a diverging lens for which the object is outside the focal point, at distance s > f. You can see all three rays appear to diverge from point P. Point P is an upright, virtual image of the object point P. h (virtual image in upright position) S h' F 1 O F 2 f S Optical axis Let s find an image distance s using the lens equation Note!!! For a diverging lens f is negative f < 0 and S > 0 is positive all the time Solve for s s is negative, so Image is virtual Let s find magnification using (And we got the same answer graphically) A positive value of m indicates that the.. image is upright relative to the object.

23 ConcepTest Diverging lens Light rays are converging to point 1. The lens is inserted into the rays with its focal point at point 1. Which picture shows the rays leaving the lens? Ray 2

24 The sign conventions Focal length, f f > 0 for a converging lens f < 0 for a diverging lens Image distance, s Magnification, m s > 0, for a real image m > 0, for an upright image s < 0, for a virtual image m < 0, for an inverted image Object distance, s s > 0 s > 0

25 ConcepTest A lens produces a sharply focused, inverted image on a screen. What will you see on the screen if the lens is covered by a dark mask having only a small hole in the center? half of the lens? Lens covered with a mask. A. An inverted but blurry image. B. An image that is dimmer but otherwise unchanged. C. Only the top half of the image. D. Only the bottom half of the image. E. No image at all. 1 screen 2 3 O F 2 F 1 Image (inverted image) Still the same image but it is created by less number of rays

26 What you should read Chapter 23 (Knight) Sections 23.4 and 23.5 skip them 23.6

27 Thank you See you on Friday