1. mirrors and lenses PHY232 Remco Zegers zegers@nscl.msu.edu Room W109 – cyclotron building http://www.nscl.msu.edu/~zegers/phy232.html

2. PHY232 - Remco Zegers - Mirrors and lenses 2 an important point  objects do not emit rays of light that get ‘seen’ by your eye. Light (from a bulb or the sun) gets reflected off the object towards your eye.

3. PHY232 - Remco Zegers - Mirrors and lenses 3 we saw…  that light can be reflected or refracted at boundaries between material with a different index of refraction.  by shaping the surfaces of the boundaries we can make devices that can focus or otherwise alter an image.  Here we focus on mirrors and lenses for which the properties can be described well by a few equations.

4. PHY232 - Remco Zegers - Mirrors and lenses 4 the flat mirror  in the previous chapter we already saw flat mirrors.  The distance from the object to the mirror the object distance p  The distance from the image to the mirror is the image distance q  in case of a flat mirror, an observer sees a virtual image, meaning that the rays do not actually come from it.  the image size (h ’ ) is the same as the object size (h), meaning that the magnification h ’ /h=1  the image is not inverted pq NOTE: a virtual image cannot be projected on a screen but is ‘visible’ by the eye or another optical instrument.

5. PHY232 - Remco Zegers - Mirrors and lenses 5 question  You are standing in front (say 1 m) of a mirror that is less high than your height. Is there a chance that you can still see your complete image?  a) yes b) no

6. PHY232 - Remco Zegers - Mirrors and lenses 6 ray diagrams  to understand the properties of optical elements we use ray diagrams, in which we draw the most important elements and parameters to understand the elements pq h h’

7. PHY232 - Remco Zegers - Mirrors and lenses 7 concave mirrors C C: center of mirror curvature a light ray passing through the center of curvature will be reflected back upon itself because it strikes the mirror normally to the surface. F: focal point F a light ray traveling parallel to the central axis of the mirror will be reflected to the focal point F, with FM=CM/2 The distance FM is called the focal length f. M

8. PHY232 - Remco Zegers - Mirrors and lenses 8 concave mirrors: an object outside F O F step 1: draw the ray from the top of the object parallel to the central axis and its reflection (through F). step 2: draw the ray from the top of the object through F and its reflection (parallel to the central axis) step 3: note that a ray from the bottom of the object just reflects back. the image of the top of the object is located where the reflected rays meet construct the image I I

9. PHY232 - Remco Zegers - Mirrors and lenses 9 concave mirrors: an object outside F O FI The image is: a)inverted (upside down) b)real (light rays pass through it) c)smaller than the object

10. PHY232 - Remco Zegers - Mirrors and lenses 10 concave mirrors: an object outside F O FI distance object-mirror: p distance image-mirror: q distance focal point-mirror: f mirror equation: 1/p + 1/q = 1/f given p,f this equation can be used to calculate q magnification: M=-q/p can be used to calculate magnification. if negative: the image is inverted if smaller than 1, object is demagnified

11. PHY232 - Remco Zegers - Mirrors and lenses 11 example  An object is placed 12 cm in front of a a concave mirror with focal length 5 cm. What are:  a) the location of the image  b) the magnification

12. PHY232 - Remco Zegers - Mirrors and lenses 12 concave mirrors: an object inside F OF step 1: draw the ray from the top of the object parallel to the central axis and its reflection (through F). step 3: note that a ray from the bottom of the object just reflects back. step 2: draw the ray from the top of the object through F and its reflection (parallel to the central axis) I the image of the top of the object is located where the reflected rays meet: in this you must draw virtual rays on the other side of the lens create the image the image is: a)not inverted b)virtual c)magnified

13. PHY232 - Remco Zegers - Mirrors and lenses 13 concave mirrors: an object inside F OFI the image is: a)not inverted b)virtual c)magnified The lens equation and equation for magnification are still valid. However, since the image is now on the other side of the mirror, its sign should be negative

14. PHY232 - Remco Zegers - Mirrors and lenses 14 example  an object is placed 2 cm in front of a lens with a focal length of 5 cm. What are the a) image distance and b) the magnification?

15. PHY232 - Remco Zegers - Mirrors and lenses 15 demo: the virtual pig

16. PHY232 - Remco Zegers - Mirrors and lenses 16 step 2: draw the ray from the top of the object through F and its reflection (parallel to the central axis) convex mirrors: an object outside F (p>|f|) O F step 3: note that a ray from the bottom of the object just reflects back. the image of the top of the object is located where the reflected rays meet construct the image I I step 1: draw the ray from the top of the object parallel to the central axis and its reflection (through F). F is now located on the other side of the mirror

17. PHY232 - Remco Zegers - Mirrors and lenses 17 convex mirrors: an object outside F (p>|f|) O FI F is now located on the other side of the mirror the image is: a)not inverted b)virtual c)demagnified The lens/mirror equation and equation for magnification are still valid. However, since the image and focal point are now on the other side of the mirror, their signs should be negative

18. PHY232 - Remco Zegers - Mirrors and lenses 18 example  an object with a height of 3 cm is placed 6 cm in front of a convex mirror, with f=-3 cm. What are a) the image distance and b) the magnification?

19. PHY232 - Remco Zegers - Mirrors and lenses 19 convex mirrors with p < |f|  the situation is exactly the same as for the situation with p > |f|. The demagnification will be different though… O F IF

20. PHY232 - Remco Zegers - Mirrors and lenses 20 Mirrors: an overview  mirror equation 1/p + 1/q = 1/f  f=R/2 where R is the radius of the mirror  magnification: M=-q/p typep?imageimage direction Mqf concavep>frealinverted|M|>0 M -++ concavep<fvirtualnot inverted |M|>1 M +-+ convexp>|f|virtualnot inverted |M|<1 M +-- convexp<|f|virtualnot inverted |M|<1 M +--

21. PHY232 - Remco Zegers - Mirrors and lenses 21 lon-capa  now do problems 7,8,11 of lon-capa 8

22. PHY232 - Remco Zegers - Mirrors and lenses 22 Lenses  Lenses function by refracting light at their surfaces  Their action depends on  radii of the curvatures of both surfaces  the refractive index of the lens  converging (positive lenses) have positive focal length and are always thickest in the center  diverging (negative lenses) have negative focal length and are thickest at the edges + - used in drawings

23. PHY232 - Remco Zegers - Mirrors and lenses 23 lensmakers equation R1R1 R2R2 f: focal length of lens n: refractive index of lens R 1 radius of front surface R 2 radius of back surface 1 2 R 2 is negative if the center of the circle is on the left of curvature 2 of the lens R 1 is positive if the center of the circle is on the right of curvature 1 of the lens object if the lens is not in air then (n lens -n medium )

24. PHY232 - Remco Zegers - Mirrors and lenses 24 example  Given R 1 =10 cm and R 2 =5 cm, what is the focal length? The lens is made of glass (n=1.5) R1R1 R2R2 1 2 object

25. PHY232 - Remco Zegers - Mirrors and lenses 25 example 2  Given R 1 =5 cm and R 2 =10 cm, what is the focal length? The lens is made of glass (n=1.5) R2R2 R1R1 1 2 object

26. PHY232 - Remco Zegers - Mirrors and lenses 26 example 3  Given R 1 =5 cm and R 2 = , what is the focal length? The lens is made of glass (n=1.5) R2R2 R1R1 1 2 object

27. PHY232 - Remco Zegers - Mirrors and lenses 27 question  A person is trying to make a lens but decides to make both surfaces flat, resulting in essentially a flat piece of glass on both sides. What is the focal length of this ‘lens’?  a) infinity  b) 0  c) cannot say, depends on the index of refraction n

28. PHY232 - Remco Zegers - Mirrors and lenses 28 converging lens p>f OF + F 1) A ray parallel to the central axis will be bend through the focal point 2) A ray through the center of the lens will continue unperturbed 3) A ray through the focal point of the lens will be bend parallel to the central axis I 4) the image is located at the crossing of the above 3 rays (you need just 2 of them). A real inverted image is created. The magnification depends on p: |M| can be 1

29. PHY232 - Remco Zegers - Mirrors and lenses 29 lens equation OF + F I The equation that connects object distance p, image distance q and focal length f is (just like for mirrors): 1/p + 1/q = 1/f Similarly for the magnification: M=-q/p q is positive if the image is on the opposite side of the lens as the object NOTE THAT THIS IS DIFFERENT THAN THE CASE FOR MIRRORS

30. PHY232 - Remco Zegers - Mirrors and lenses 30 example  an object is put 20 cm in front of a positive lens, with focal length of 12 cm. a) What is the image distance q? b) What is the magnification?

31. PHY232 - Remco Zegers - Mirrors and lenses 31 converging lens p<f OF + F A virtual non-inverted image is created. Magnification >1 1) A ray parallel to the central axis will be bend through the focal point 3) A ray through the focal point of the lens will be bend parallel to the central axis 2) A ray through the center of the lens will continue unperturbed 4) the image is located at the crossing of the above 3 rays (you need just 2 of them). I

32. PHY232 - Remco Zegers - Mirrors and lenses 32 example  an object is put 2 cm in front of a positive lens, with focal length of 3 cm. a) What is the image distance q? b) What is the magnification?

33. PHY232 - Remco Zegers - Mirrors and lenses 33 question  An object is placed in front of a converging (positive) lens with the object distance larger than the focal distance. An image is created on a screen on the other side of the lens. Then, the lower half of the lens is covered with a piece of wood. Which of the following is true:  a) the image on the screen will become less bright only  b) half of the image on the screen will disappear only  c) half of the image will disappear and the remainder of the image will become less bright.

34. PHY232 - Remco Zegers - Mirrors and lenses 34 NOT CORRECT

35. PHY232 - Remco Zegers - Mirrors and lenses 35 diverging lens p>|f| OF - F 2) A ray through the center of the lens will continue unperturbed I 4) the image is located at the crossing of the above 3 rays (you need just 2 of them). A virtual non-inverted image is created. The magnification |M|<1 1)A ray parallel to the central axis will be bend so that the ray passes through the focal point IN FRONT of the lens 3) A ray aimed at the focal point on the other side of the lens will be bent parallel to the central axis

36. PHY232 - Remco Zegers - Mirrors and lenses 36 example  an object is put 5 cm in front of a negative lens, with focal length of -3 cm. a) What is the image distance q? b) What is the magnification?

37. PHY232 - Remco Zegers - Mirrors and lenses 37 diverging lens p<|f| O F - F 2) A ray through the center of the lens will continue unperturbed A virtual non-inverted image is created. The magnification |M| |f| 1)A ray parallel to the central axis will be bend so that the ray passes through the focal point IN FRONT of the lens 3) A ray aimed at the focal point on the other side of the lens will be bent parallel to the central axis I 4) the image is located at the crossing of the above 3 rays (you need just 2 of them).

38. PHY232 - Remco Zegers - Mirrors and lenses 38 example  an object is put 2 cm in front of a negative lens, with focal length of -3 cm. a) What is the image distance q? b) What is the magnification?

39. PHY232 - Remco Zegers - Mirrors and lenses 39 lenses, an overview typep?imageimage direction Mqf converging p>frealinverted|M|>0 M -++ converging p<fvirtualnot inverted |M|>1 M +-+ diverging p>|f|virtualnot inverted |M|<1 M +-- diverging p<|f|virtualnot inverted |M|<1 M +--  mirror equation 1/p + 1/q = 1/f  magnification: M=-q/p  lens makers equation: 1/f=(n-1)(1/R 1 -1/R 2 )

40. PHY232 - Remco Zegers - Mirrors and lenses 40 spherical aberrations: Hubble space telescope spherical aberrations are due to the rays hitting the lens at different locations have a different focal point perfect distorted example: Hubble before after correction

41. PHY232 - Remco Zegers - Mirrors and lenses 41 chromatic aberrations Chromatic aberrations are due to light of different wavelengths having a different index of refraction Can be corrected by combining lenses/mirrors If n varies with wavelength, the focal length f changes with wavelength

42. PHY232 - Remco Zegers - Mirrors and lenses 42 two lenses  an object, 1 cm high, is placed 5 cm in front of a converging mirror with a focal length of 3 cm. This setup is placed in front of a diverging mirror with a focal length of –5 cm. The distance between the two lenses is 10 cm. Where is the image located, and what are its properties? +- 5 cm 3cm 15 cm 5cm

43. PHY232 - Remco Zegers - Mirrors and lenses 43 lon-capa  now do problems 9,10,12 of lon-capa 8