Vergence The Vergence Formula Basic Optics Chapter 3

Vergence: The Vergence Formula Basic Optics, Chapter 3

2 Vergence: The Vergence Formula A +1 D lens will focus parallel rays 1 m to the right of the lens +1 D Distance = 1 m Reciprocal = 1/1 Diopters = +1 1 meter We have seen how the dioptric power of a lens affects incoming parallel rays. A -1 D lens will ‘focus’ parallel rays 1 m to the left of the lens -1 D Distance = -1 m Reciprocal = 1/-1 Diopters = -1 -1 meter (Remember, distances to the left of the lens are considered ‘minus’)

3 Vergence: The Vergence Formula non +1 D ^ A +1 D lens will focus parallel rays ? m to the ? of the lens ? Diopters = +1 Reciprocal = ? Distance = ? We have seen how the dioptric power of a lens affects incoming parallel rays. But what if the rays are not parallel? non ^ A -1 D lens will ‘focus’ parallel rays ? m to the ? of the lens -1 D ? Diopters = -1 Reciprocal = ? Distance = ?

4 Vergence: The Vergence Formula non +1 D ^ A +1 D lens will focus parallel rays ? m to the ? of the lens ? Diopters = +1 Reciprocal = ? Distance = ? We have seen how the dioptric power of a lens affects incoming parallel rays. But what if the rays are not parallel? We need a more generalized concept concerning the relationships among incoming/outgoing rays, and lenses. non ^ A -1 D lens will ‘focus’ parallel rays ? m to the ? of the lens -1 D ? Diopters = -1 Reciprocal = ? Distance = ?

5 Vergence: The Vergence Formula non +1 D ^ A +1 D lens will focus parallel rays ? m to the ? of the lens ? Diopters = +1 Reciprocal = ? Distance = ? We have seen how the dioptric power of a lens affects incoming parallel rays. But what if the rays are not parallel? We need a more generalized concept concerning the relationships among incoming/outgoing rays, and lenses. This is provided by The Vergence Formula non ^ A -1 D lens will ‘focus’ parallel rays ? m to the ? of the lens -1 D ? Diopters = -1 Reciprocal = ? Distance = ?

6 Vergence: The Vergence Formula l The Vergence Formula

7 Vergence: The Vergence Formula l Crucial concept in optics

8 Vergence: The Vergence Formula l l Crucial concept in optics Describes the vergence relations among rays before, during and after encountering a refractive surface (e. g. , lens)

9 Vergence: The Vergence Formula l l Crucial concept in optics Describes the vergence relations among rays before, during and after encountering a refractive surface (e. g. , lens) l Head’s up: We will also use the Vergence Formula in describing the relations among rays interacting with reflecting surfaces, i. e. , mirrors

10 Vergence: The Vergence Formula l The Vergence Formula U+P=V

11 Vergence: The Vergence Formula l The Vergence Formula Vergence of incoming light (in diopters) U+P=V

12 Vergence: The Vergence Formula l The Vergence Formula Vergence of incoming light (in diopters) Vergence contributed by lens (in diopters) U+P=V

13 Vergence: The Vergence Formula l The Vergence Formula Vergence of incoming light (in diopters) Vergence contributed by lens (in diopters) U+P=V Vergence of light leaving lens (in diopters)

14 Vergence: The Vergence Formula l The Vergence Formula Vergence of incoming light (in diopters) Vergence contributed by lens (in diopters) Vergence of light leaving lens (in diopters) U+P=V tl; dr The vergence of light leaving a lens is the sum of the vergence of the light entering the lens and the vergence contributed by the lens itself

15 Vergence: The Vergence Formula U+P=V +1 D Parallel rays, therefore U=0

16 Vergence: The Vergence Formula U+P=V +1 D lens, therefore P = +1 D Parallel rays, therefore U=0 P=+1 D

17 Vergence: The Vergence Formula U+P=V Plugging these values into the Vergence Formula: U+P=V 0 + (+1) = V +1 D lens, therefore P = +1 D Parallel rays, therefore U=0 P=+1 D

18 Vergence: The Vergence Formula U+P=V Plugging these values into the Vergence Formula: U+P=V 0 + (+1) = V +1 D Parallel rays, therefore U=0 P=+1 D V = +1 D

19 Vergence: The Vergence Formula U+P=V Plugging these values into the Vergence Formula: U+P=V 0 + (+1) = V +1 D Parallel rays, therefore U=0 P=+1 D V = +1 D Distance? Distance equals the reciprocal of the outgoing vergence, ie, 1/V

20 Vergence: The Vergence Formula U+P=V Plugging these values into the Vergence Formula: U+P=V 0 + (+1) = V +1 D Parallel rays, therefore U=0 P=+1 D V = +1 D 1/+1 = 1 meter Distance equals the reciprocal of the outgoing vergence, ie, 1/V

21 Vergence: The Vergence Formula U+P=V +2 D U=0 P=+2 D V=?

22 Vergence: The Vergence Formula U+P=V +2 D U=0 P=+2 D V = +2 D Distance = ?

23 Vergence: The Vergence Formula U+P=V +2 D U=0 P=+2 D V = +2 D Distance = 1/2 =. 5 m

24 Vergence: The Vergence Formula U+P=V +3 D U=? -. 4 meters P=+3 D To determine the vergence U of the incoming light, take the reciprocal of the distance from its source or focal point:

25 Vergence: The Vergence Formula U+P=V +3 D U = 1/-. 4 m = -2. 5 D P=+3 D Remember, the vergence of diverging rays is always negative! -. 4 meters To determine the vergence U of the incoming light, take the reciprocal of the distance from its source or focal point: U = 1/-. 4 m = -2. 5 D

26 Vergence: The Vergence Formula U+P=V Plugging these values into the Vergence Formula: U+P=V -2. 5 + (+3) = V +0. 5 = V +3 D U = -2. 5 D P=+3 D -. 4 meters V = +0. 5 D

27 Vergence: The Vergence Formula U+P=V Plugging these values into the Vergence Formula: U+P=V -2. 5 + (+3) = V +0. 5 = V +3 D U = -2. 5 D P=+3 D -. 4 meters V = +0. 5 D Distance = ? Distance equals the reciprocal of the outgoing vergence, ie, 1/V

28 Vergence: The Vergence Formula U+P=V Plugging these values into the Vergence Formula: U+P=V -2. 5 + (+3) = V +0. 5 = V +3 D U = -2. 5 D P=+3 D -. 4 meters V = +0. 5 D Distance = 1/. 5 = 2 m Distance equals the reciprocal of the outgoing vergence, ie, 1/V

29 Vergence: The Vergence Formula U+P=V -1 D U = 1/-1 m = -1 D -1 meter P= -1 D

30 Vergence: The Vergence Formula U+P=V Plugging these values into the Vergence Formula: U+P=V -1 + (-1) = V -2 = V -1 D U = 1/-1 m = -1 D -1 meter P= -1 D V = -2 D

31 Vergence: The Vergence Formula U+P=V Plugging these values into the Vergence Formula: U+P=V -1 + (-1) = V -2 = V -1 D P= -1 D U = 1/-1 m = -1 D -1 meter 1/-2 = -. 5 meters V = -2 D

32 Vergence: The Vergence Formula U+P=V Plugging these values into the Vergence Formula: Note that the cartoon seems to indicate that the lens causes the rays to originate from this point. This of course is not what happens. Nonetheless, the lens does cause the exiting rays to diverge as if they did! Weirder still, this point is considered a focal point, even though the rays act as if they are leaving, not approaching it. More shortly! U+P=V -1 + (-1) = V -2 = V -1 D P= -1 D U = 1/-1 m = -1 D -1 meter 1/-2 = -. 5 meters V = -2 D

33 Vergence: The Vergence Formula U+P=V -1 D U=? P= -1 D To determine U, we need to know…

34 Vergence: The Vergence Formula U+P=V The vergence of converging rays is always positive! U = 1/+0. 5 = +2 D -1 D P= -1 D +0. 5 meters To determine U, we need to know…this distance.

35 Vergence: The Vergence Formula U+P=V Plugging these values into the Vergence Formula: U+P=V +2 + (-1) = V +1 = V -1 D U = 1/+0. 5 = +2 D P= -1 D +0. 5 meters Distance = 1/V = 1/1 = 1 meter

36 An object. Vergence is located ½ m to the left of a +4 D lens, which Vergence: The Formula is in turn 1 m to the left of a +3 D lens. Where will the U+P=V final image be with respect to the second lens? ? 1 m to the right of the second lens. To solve vergence problems such as this one, the key is to solve U+P=V for the first lens, then treat the image thus produced as the object for the next lens. This can be continued for any number of lenses. +4 D +3 D Object -0. 5 m 1 m

37 An object. Vergence is located ½ m to the left of a +4 D lens, which Vergence: The Formula is in turn 1 m to the left of a +3 D lens. Where will the U+P=V final image be with respect to the second lens? ? 1 m to the right of the second lens. To solve vergence problems such as this one, the key is to solve U+P=V for the first lens, then treat the image thus produced as the object for the next lens. This can be continued for any number of lenses. +4 D +3 D Object -0. 5 m 1 m

38 An object. Vergence is located ½ m to the left of a +4 D lens, which Vergence: The Formula is in turn 1 m to the left of a +3 D lens. Where will the U+P=V final image be with respect to the second lens? ? 1 m to the right of the second lens. To solve vergence problems such as this one, the key is to solve U+P=V for the first lens, then treat the image thus produced as the object for the next lens. This can be continued for any number of lenses. For the +4 D lens: U = 1/-0. 5 = -2 D P = +4 V = +2 The image from the first lens is 1/2 =. 5 m to the right of the first lens +4 D +3 D Object -0. 5 m 1 m

39 An object. Vergence is located ½ m to the left of a +4 D lens, which Vergence: The Formula is in turn 1 m to the left of a +3 D lens. Where will the U+P=V final image be with respect to the second lens? ? 1 m to the right of the second lens. To solve vergence problems such as this one, the key is to solve U+P=V for the first lens, then treat the image thus produced as the object for the next lens. This can be continued for any number of lenses. For the +4 D lens: U = 1/-0. 5 = -2 D P = +4 D V = +2 The image from the first lens is 1/2 =. 5 m to the right of the first lens +4 D +3 D Object -0. 5 m 1 m

40 An object. Vergence is located ½ m to the left of a +4 D lens, which Vergence: The Formula is in turn 1 m to the left of a +3 D lens. Where will the U+P=V final image be with respect to the second lens? ? 1 m to the right of the second lens. To solve vergence problems such as this one, the key is to solve U+P=V for the first lens, then treat the image thus produced as the object for the next lens. This can be continued for any number of lenses. For the +4 D lens: U = 1/-0. 5 = -2 D P = +4 D V = -2 + (+4) = +2 D The image from the first lens is 1/2 =. 5 m to the right of the first lens +4 D +3 D Object -0. 5 m 1 m

41 An object. Vergence is located ½ m to the left of a +4 D lens, which Vergence: The Formula is in turn 1 m to the left of a +3 D lens. Where will the U+P=V final image be with respect to the second lens? ? 1 m to the right of the second lens. To solve vergence problems such as this one, the key is to solve U+P=V for the first lens, then treat the image thus produced as the object for the next lens. This can be continued for any number of lenses. For the +4 D lens: U = 1/-0. 5 = -2 D P = +4 D V = -2 + (+4) = +2 D The image from the first lens is 1/2 =. 5 m to the right of the first lens +4 D +3 D Object Image 0. 5 m -0. 5 m 1 m

42 An object. Vergence is located ½ m to the left of a +4 D lens, which Vergence: The Formula is in turn 1 m to the left of a +3 D lens. Where will the U+P=V final image be with respect to the second lens? ? 1 m to the right of the second lens. To solve vergence problems such as this one, the key is to solve U+P=V for the first lens, then treat the image thus produced as the object for the next lens. This can be continued for any number of lenses. For the +4 D lens: U = 1/-0. 5 = -2 D P = +4 D V = -2 + (+4) = +2 D The image from the first lens is 1/2 =. 5 m to the right of the first lens +4 D For the +3 D lens: U = 1/-0. 5 = -2 D P = +3 V = +1 The image formed by the second lens is 1/1 = 1 m to the right of the second lens +3 D Object Image 0. 5 m -0. 5 m 1 m

43 An object. Vergence is located ½ m to the left of a +4 D lens, which Vergence: The Formula is in turn 1 m to the left of a +3 D lens. Where will the U+P=V final image be with respect to the second lens? ? 1 m to the right of the second lens. To solve vergence problems such as this one, the key is to solve U+P=V for the first lens, then treat the image thus produced as the object for the next lens. This can be continued for any number of lenses. For the +4 D lens: U = 1/-0. 5 = -2 D P = +4 D V = -2 + (+4) = +2 D The image from the first lens is 1/2 =. 5 m to the right of the first lens +4 D For the +3 D lens: U = 1/-0. 5 = -2 D P = +3 D V = +1 The image formed by the second lens is 1/1 = 1 m to the right of the second lens +3 D Object Image 0. 5 m -0. 5 m 1 m

44 An object. Vergence is located ½ m to the left of a +4 D lens, which Vergence: The Formula is in turn 1 m to the left of a +3 D lens. Where will the U+P=V final image be with respect to the second lens? ? 1 m to the right of the second lens. To solve vergence problems such as this one, the key is to solve U+P=V for the first lens, then treat the image thus produced as the object for the next lens. This can be continued for any number of lenses. For the +4 D lens: U = 1/-0. 5 = -2 D P = +4 D V = -2 + (+4) = +2 D The image from the first lens is 1/2 =. 5 m to the right of the first lens +4 D For the +3 D lens: U = 1/-0. 5 = -2 D P = +3 D V = -2 + (+3) = +1 D The image formed by the second lens is 1/1 = 1 m to the right of the second lens +3 D Object Image 0. 5 m -0. 5 m 1 m

45 An object. Vergence is located ½ m to the left of a +4 D lens, which Vergence: The Formula is in turn 1 m to the left of a +3 D lens. Where will the U+P=V final image be with respect to the second lens? ? 1 m to the right of the second lens. To solve vergence problems such as this one, the key is to solve U+P=V for the first lens, then treat the image thus produced as the object for the next lens. This can be continued for any number of lenses. For the +4 D lens: U = 1/-0. 5 = -2 D P = +4 D V = -2 + (+4) = +2 D The image from the first lens is 1/2 =. 5 m to the right of the first lens +4 D For the +3 D lens: U = 1/-0. 5 = -2 D P = +3 D V = -2 + (+3) = +1 D The image formed by the second lens is 1/1 = 1 m to the right of the second lens +3 D Object Image 0. 5 m -0. 5 m Image -0. 5 m 1 m 1 m

46 An object. Vergence is located ½ m to the left of a -2 D lens, Vergence: The Formula which is in turn 1 m to the left of a +1 D lens. How far is the final image from the object? U+P=V -2 D +1 D Object -0. 5 m 1 m

47 An object. Vergence is located ½ m to the left of a -2 D lens, Vergence: The Formula which is in turn 1 m to the left of a +1 D lens. How far is the final image from the object? 6. 50 m. U+P=V For the -2 D lens: U = 1/-0. 5 = -2 D +1 D Object -0. 5 m 1 m

48 An object. Vergence is located ½ m to the left of a -2 D lens, Vergence: The Formula which is in turn 1 m to the left of a +1 D lens. How far is the final image from the object? 6. 50 m. U+P=V For the -2 D lens: U = 1/-0. 5 = -2 D P = -2 D +1 D Object -0. 5 m 1 m

49 An object. Vergence is located ½ m to the left of a -2 D lens, Vergence: The Formula which is in turn 1 m to the left of a +1 D lens. How far is the final image from the object? 6. 50 m. U+P=V For the -2 D lens: U = 1/-0. 5 = -2 D P = -2 D V = -2 + (-2) = -4 D -2 D +1 D Object -0. 5 m 1 m

50 An object. Vergence is located ½ m to the left of a -2 D lens, Vergence: The Formula which is in turn 1 m to the left of a +1 D lens. How far is the final image from the object? 6. 50 m. U+P=V For the -2 D lens: U = 1/-0. 5 = -2 D P = -2 D V = -2 + (-2) = -4 D The image from the first lens is 1/-4 =. 25 m to the left of the first lens -2 D Image +1 D Object -. 25 m -0. 5 m 1 m

51 An object. Vergence is located ½ m to the left of a -2 D lens, Vergence: The Formula which is in turn 1 m to the left of a +1 D lens. How far is the final image from the object? 6. 50 m. U+P=V For the -2 D lens: U = 1/-0. 5 = -2 D P = -2 D V = -4 D The image from the first lens is 1/-4 =. 25 m to the left of the first lens Object Image For the +1 D lens: U = 1/-1. 25 m = -0. 8 D P = +1 V = +0. 2 The image formed by the second lens is 1/+0. 2 = 5 m to the right of the second lens -2 D +1 D Object -. 25 m -0. 5 m 1 m -1. 25 m

52 An object. Vergence is located ½ m to the left of a -2 D lens, Vergence: The Formula which is in turn 1 m to the left of a +1 D lens. How far is the final image from the object? 6. 50 m. U+P=V For the -2 D lens: U = 1/-0. 5 = -2 D P = -2 D V = -4 D The image from the first lens is 1/-4 =. 25 m to the left of the first lens Object Image For the +1 D lens: U = 1/-1. 25 m = -0. 8 D P = +1 D V = +0. 2 The image formed by the second lens is 1/+0. 2 = 5 m to the right of the second lens -2 D +1 D Object -. 25 m -0. 5 m 1 m -1. 25 m

53 An object. Vergence is located ½ m to the left of a -2 D lens, Vergence: The Formula which is in turn 1 m to the left of a +1 D lens. How far is the final image from the object? 6. 50 m. U+P=V For the -2 D lens: U = 1/-0. 5 = -2 D P = -2 D V = -4 D The image from the first lens is 1/-4 =. 25 m to the left of the first lens Object Image For the +1 D lens: U = 1/-1. 25 m = -0. 8 D P = +1 D V = -0. 8 + (+1) = +0. 2 D The image formed by the second lens is 1/+0. 2 = 5 m to the right of the second lens -2 D +1 D Object -. 25 m -0. 5 m 1 m -1. 25 m

54 An object. Vergence is located ½ m to the left of a -2 D lens, Vergence: The Formula which is in turn 1 m to the left of a +1 D lens. How far is the final image from the object? 6. 50 m. U+P=V For the -2 D lens: U = 1/-0. 5 = -2 D P = -2 D V = -4 D The image from the first lens is 1/-4 =. 25 m to the left of the first lens Object Image For the +1 D lens: U = 1/-1. 25 m = -0. 8 D P = +1 D V = -0. 8 + (+1) = +0. 2 D The image formed by the second lens is 1/+0. 2 = 5 m to the right of the second lens -2 D +1 D Object Image -. 25 m -0. 5 m 1 m -1. 25 m 5 m

55 An object. Vergence is located ½ m to the left of a -2 D lens, Vergence: The Formula which is in turn 1 m to the left of a +1 D lens. How far is the final image from the object? 6. 50 m U+P=V For the -2 D lens: U = 1/-0. 5 = -2 D P = -2 D V = -4 D The image from the first lens is 1/-4 =. 25 m to the left of the first lens Object Image For the +1 D lens: U = 1/-1. 25 m = -0. 8 D P = +1 D V = -0. 8 + (+1) = +0. 2 D The image formed by the second lens is 1/+0. 2 = 5 m to the right of the second lens -2 D Distance from object to image = 6. 50 m +1 D Object Image -. 25 m -0. 5 m 1 m 5 m -1. 25 m 6. 50 m

56 An object. Vergence is located ½ m to the left of a -2 D lens, Vergence: The Formula which is in turn 1 m to the left of a +1 D lens. How far is the final image from the object? 6. 50 m U+P=V But-2 D it looks object have to pass through the -2 D lens For the lens: like the rays from the first image/second For the +1 D lens: twice =before reaching the +1 D lens. Doesn’t this refract those rays again? U = 1/-0. 5 -2 U = 1/-1. 25 m = -0. 8 NO. After the light bouncing off the physical object passes through the -2 D lens, it Distance acts as if itfrom object P = -2 P = +1 camepass fromthrough the first image/second object In fact, = 6. 50 m First the lens V = -4 to image V location, = +0. 2 but it’s not really coming from there. The image the first lens clinical is 1/-4 optics is. The as we from will come to see, lessimage a description what light does than it is from theofsecond lensactually is 1/+0. 2 =. 25 ampowerful to the left of the first lens metaphor that allows us to make useful (and prescriptions!) of what =5 m to the descriptions right of the second lens Second pass through the lens? light does. In essence, clinical optics is a convenient fiction. More on this (much) later. Object Image -2 D +1 D Object Image -. 25 m -0. 5 m 1 m 5 m -1. 25 m 6. 50 m

57 An object. Vergence is located ½ m to the left of a -2 D lens, Vergence: The Formula which is in turn 1 m to the left of a +1 D lens. How far is the final image from the object? 6. 50 m U+P=V But-2 D it looks object have to pass through the -2 D lens For the lens: like the rays from the first image/second For the +1 D lens: twice =before reaching the +1 D lens. Doesn’t this refract those rays again? U = 1/-0. 5 -2 U = 1/-1. 25 m = -0. 8 NO. After the light bouncing off the physical object passes through the -2 D lens, it Distance acts as if itfrom object P = -2 P = +1 came from the first image/second object In fact, = 6. 50 m V = -4 to image V location, = +0. 2 but it’s not really coming from there. The image the first lens clinical is 1/-4 optics is. The as we from will come to see, lessimage a description what light does than it is from theofsecond lensactually is 1/+0. 2 =. 25 ampowerful to the left of the first lens metaphor that allows us to = make descriptions (and prescriptions!) of what 5 m useful to the right of the second lens light does. In essence, clinical optics is a convenient fiction. More on this (much) later. Object Image -2 D +1 D Object Image -. 25 m -0. 5 m 1 m 5 m -1. 25 m 6. 50 m

58 An object. Vergence is located ½ m to the left of a -2 D lens, Vergence: The Formula which is in turn 1 m to the left of a +1 D lens. How far is the final image from the object? 6. 50 m. OK, but there’s another problem. Clearly, the rays that have passed through the -2 D are far too divergent to pass through the +1 D lens—they’re going to miss it by a mile! How can these rays possibly be refracted by the second lens? Don’t let such ‘drawing artifacts’ fool you—some of the light will make it through the second lens. U+P=V For the -2 D lens: U = 1/-0. 5 = -2 D P = -2 D V = -4 D The image from the first lens is 1/-4 =. 25 m to the left of the first lens Object Image For the +1 D lens: U = 1/-1. 25 m = -0. 8 D Distance from object P = +1 D to image = 6. 50 m V = +0. 2 D The image from the second lens is 1/+0. 2 = 5 m to the right of the second lens -2 D +1 D Object Image -. 25 m -0. 5 m 1 m 5 m -1. 25 m 6. 50 m

59 An object. Vergence is located ½ m to the left of a -2 D lens, Vergence: The Formula which is in turn 1 m to the left of a +1 D lens. How far is the final image from the object? 6. 50 m. OK, but there’s another problem. Clearly, the rays that have passed through the -2 D are far too divergent to pass through the +1 D lens—they’re going to miss it by a mile! How can these rays possibly be refracted by the second lens? Don’t let such ‘drawing artifacts’ fool you—some of the light will make it through the second lens. U+P=V For the -2 D lens: U = 1/-0. 5 = -2 D P = -2 D V = -4 D The image from the first lens is 1/-4 =. 25 m to the left of the first lens Object Image For the +1 D lens: U = 1/-1. 25 m = -0. 8 D Distance from object P = +1 D to image = 6. 50 m V = +0. 2 D The image from the second lens is 1/+0. 2 = 5 m to the right of the second lens -2 D +1 D Object Image -. 25 m -0. 5 m 1 m 5 m -1. 25 m 6. 50 m

60 An object. Vergence is located ½ m to the left of a -2 D lens, Vergence: The Formula which is in turn 1 m to the left of a +1 D lens. How far is the final image from the object? 6. 50 m. OK, but there’s another problem. Clearly, the rays that have passed through the -2 D are far too divergent to pass through the +1 D lens—they’re going to miss it by a mile. How can these rays possibly be refracted by the second lens? Don’t let such ‘drawing artifacts’ fool you—some of the light will make it through the second lens. U+P=V In fact, to make this point explicitly, illustrators will For the -2 D lens: use dashed lines to ‘extend’For sometimes a lens so lens: the +1 D U = 1/-0. 5 = -2 as to capture the rays in question. U = 1/-1. 25 m = -0. 8 D P = -2 D Distance from object P = +1 D V = -4 D to image = 6. 50 m V = +0. 2 D The image from the first lens is 1/-4 The image from the second lens is 1/+0. 2 =. 25 m to the left of the first lens = 5 m to the right of the second lens Object Image -2 D +1 D Object Image -. 25 m -0. 5 m 1 m 5 m -1. 25 m 6. 50 m

61 Vergence: The Vergence Formula 1 D 1 meter l The ability of a lens to induce vergence is expressed in diopters l Dioptric power of a lens: The reciprocal of the distance (in meters) to the point where incoming parallel light rays would intersect after passing through the lens We encountered this slide a few minutes ago… The notion that a diopter does something to light over the course of a meter should remind you of the effect a prism has on light…

62 Vergence: The Vergence Formula 1 D 1 meter 1 PD 1 cm (Obviously not to scale) 1 meter A prism diopter (PD, or D) displaces light 1 cm at 1 meter.

63 Vergence: The Vergence Formula 1 D 1 meter 1 PD 1 cm (Obviously not to scale) 1 meter A prism diopter (PD, or D) displaces light 1 cm at 1 meter. Which do prisms induce: convergence or divergence? Neither--prisms do not induce vergence! Prisms cause light rays to change direction, but not to converge or diverge.

64 Vergence: The Vergence Formula 1 D 1 meter 1 PD 1 cm (Obviously not to scale) 1 meter A prism diopter (PD, or D) displaces light 1 cm at 1 meter. Which do prisms induce: convergence or divergence? Neither--prisms do not induce vergence! Prisms cause light rays to change direction, but not to converge or diverge.

65 Vergence: The Vergence Formula 1 D 1 meter 1 PD 1 cm (Obviously not to scale) 1 meter But, if we placed two prisms base-to-base or apex-to-apex, we could get light to converge and diverge, respectively

66 Vergence: The Vergence Formula 1 D 1 meter 1 PD 1 cm (Obviously not to scale) 1 meter = In fact, we will at times find it very useful to think of lenses as being composed of prisms arranged in just this manner! =

67 Vergence: The Vergence Formula Of course, prisms also disperse white light into its component colors. They do this because the different wavelengths are refracted different amounts. And because they are composed of prisms… lenses do too.

68 Vergence: The Vergence Formula Of course, prisms also disperse white light into its component colors. They do this because the different wavelengths are refracted different amounts. And because they are composed of prisms…lenses do too.

69 Vergence: The Vergence Formula As we shall see in a later chapter, this property accounts for an important ocular phenomenon called chromatic aberration.