1. Chapter 34: Thin Lenses 1 Now consider refraction through this piece of glass: optic axis This is called a “Double Convex Lens” converging light focal point refraction occurs here

2. Chapter 34: Thin Lenses 2 Converging Lenses (convex) Diverging Lenses (concave)

3. Chapter 34: Thin Lenses 3 Converging Lens The focal point is visible because real rays go through it. Diverging Lens Where is the focal point for these 4 incoming rays? Don’t confuse these reflections for something meaningful.

4. Chapter 34: Thin Lenses 4 Optical Ray Diagram: a line drawing depicting a small number of key light rays. For a lens, an optical ray diagram should include: 1.Parallel Ray. A ray parallel to the optic axis which passes through the object & the focal point. 2.Focal Ray. A ray that passes through both the focal point and the object. 3.Chief Ray. A ray that passes through both the center of the lens and the object. These three rays intersect at the image. Note: we don’t use reflected rays in lens analysis.

5. Chapter 34: Thin Lenses 5 The Diverging Lens  parallel ray virtual part real part Virtual part: where the refracted ray appears to come from. ff

6. Chapter 34: Thin Lenses 6 The Diverging Lens  virtual part real part focal ray Virtual part: where the refracted ray appears to come from.

7. Chapter 34: Thin Lenses 7 The Diverging Lens  chief ray The chief ray has no virtual part.

8. Chapter 34: Thin Lenses 8  Put all three rays together: The three refracted rays have no intersection.

9. Chapter 34: Thin Lenses 9  Put all three rays together: There is an intersection of the virtual parts. Need virtual parts to find the image?  Virtual image. upright image object focal point

10. Chapter 34: Thin Lenses 10  Parallel ray Chief ray Focal ray soso f sisi a converging lens The Thin Lens Equation

11. Chapter 34: Thin Lenses 11  Parallel ray Chief ray Focal ray a converging lens Positive side for object distance Negative side for image distance focal length (e.g. diverging lens) Positive side for image distance focal length Opposite for mirrors The Thin Lens Equation

12. Chapter 34: Thin Lenses 12 The Thin Lens Equation “Strength” or “Power” of lens f, s o and d i all must have the same length units. Units of P usually in [m -1 ] or rather [Diopters]. Note: our book uses “P”. Other books use “S”.

13. Chapter 34: Thin Lenses 13 Why is 1/f called the “lens power”? focal point at  (or sometimes “strength”) “approaches”

14. Chapter 34: Thin Lenses 14 focal point very close to the lens Why is 1/f called the “lens power”? (or sometimes “strength”) “approaches”

15. Chapter 34: Thin Lenses 15 Example 1: A lens focuses light from an object 2.75m away as an image 0.483m on the other side of the lens. What are the focal length, lens type and image type? The lens is converging because:  f>0 Converging lens: f>0 Diverging lens: f<0 What is the image type?

16. Chapter 34: Thin Lenses 16 The image is real (s i >0). Is it inverted or upright?  Ray diagram shows the image is:  Real  Inverted True whenever the object is outside the focal point of a converging lens. 2.75 m 0.411m 0.483m 6 cm = 1m

17. Chapter 34: Thin Lenses 17  The ray diagram also shows the image is small. hoho hihi Magnification: Minus sign indicates that real images are always inverted. positive side for d i and f negative side for d i and f

18. Chapter 34: Thin Lenses 18 How to do lens problems graphically 1. Use a full sheet – Landscape. 2. Sketch the lens on the optic axis. 3. Sketch the objects – correctly positioned. 4. Show a scale. You might wish to show a different scale for vertical and horizontal lengths 5. Sketch two principle rays per object and find the image. 6. Refraction occurs on the vertical center-line.

19. Chapter 34: Thin Lenses 19 Example 2: How far from a converging lens with a focal length of 25 cm should an object be placed to produce a real image which is the same size as the object? (Minus because all real images are inverted.) s i >0

20. Chapter 34: Thin Lenses 20 How to make a magnifying glass What kind of lens has an upright image with m>1?  s i <0 f Place the object within the focal length of a converging lens.  s i negative  |s i | > |s o | image is farther from the lens than the object