1. How Does a Lens Work? Light travels slower in the lens material than in the air around it. This means a linear light wave will be bent by the lens due to the varying thickness of the lens.

2. How Does a Lens Work? The light wave either converges or diverges depending on the type of lens.

3. Types of Lenses There are two general types of lenses based on their effect on incident light. –Converging Lenses Known as a Convex Lens Thicker in the middle that at the edge

4. Types of Lenses There are two general types of lenses based on their effect on incident light. –Diverging Lenses Known as a Concave Lens Thicker at the edge than in the middle

5. Convex Lens Ray Diagram

6. Concave Lens Ray Diagram

7. Image Formation Focal Length (f) is the distance between the optical center and the principal focus of the lens.

8. Image Formation Focal Plane is a plane perpendicular to the principal axis at the principal focus that is incident to the light rays at a small angle from the principal axis.

9. Images Formed by Converging Lenses Case 1: Objects at an Infinite Distance –Incoming rays essentially parallel to the principal axis –Image is a point at the real focus

10. Images Formed by Converging Lenses Case 2: Object at a Finite Distance beyond Twice the Focal Length –Image is real, inverted, reduced, and located between the focus and twice the focus distance on the opposite side of the lens

11. Images Formed by Converging Lenses Case 3: Object at a Distance Equal to Twice the Focal Length –Image is real, inverted, the same size as the object and located twice the focal length on the opposite side of the lens

12. Images Formed by Converging Lenses Case 4: Object at a Distance between One and Two Focal Lengths Away –Image is real, inverted, enlarged, and located beyond twice the focal length on the opposite side of the lens

13. Images Formed by Converging Lenses Case 5: Object at the Principal Focus –No Image Formed

14. Images Formed by Converging Lenses Case 6: Object at a Distance of less than One Focal Length Away –Image is virtual, erect, enlarged, and located on the same side of the lens as the object

15. Images Formed by Diverging Lenses Only one type of image is formed that is virtual, erect, and reduced in size

16. Object-Image Relationships For thin lenses, the ratio of the object size to the image size is equal to the ratio of the object distance to the image distance.

17. Object-Image Relationships This is given by the equation: h i /h o = d i /d o –Where: h is the height of the object or image d is the distance of the object or image

18. Object-Image Relationships The inverse of the focal length is equal to the sum of the inverse of the distance to the object and the inverse of the distance to the image.

19. Object-Image Relationships This is given by the equation: 1/f = (1/d o ) + (1/d i ) –Where: f is the focal length d is the distance to the object or the image

20. Object-Image Relationships The lens equation for focal length is valid provided these sign conventions are followed: –d o is positive for real objects negative for virtual objects –d i is positive for real images negative for virtual images

21. Object-Image Relationships The lens equation for focal length is valid provided these sign conventions are followed: –f is positive for converging (convex) lenses negative for diverging (concave) lenses

22. Magnification (M) Magnification is defined as the ratio of the image height to the object height. M = h i /h o since the height ratio is equal to the distance ratio, magnification can also be defined as; M = d i /d o

23. Magnification (M) The point nearest to the eye where a distinct image can be formed is called the near point (assumed to be 25 cm). A lens placed just inside the focal point will produce a magnified image at the near point.

24. Magnification (M) The magnification of this image can be calculated using the equation; M = 25 cm/f This equation can be modified to solve for the focal length giving the equation; f = 25 cm/M