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Ch 34: Geometric OpticsWorksheetSee all chapters

# Ray Diagrams For Lenses

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Sections
Ray Nature Of Light
Reflection Of Light
Refraction Of Light
Total Internal Reflection
Ray Diagrams For Mirrors
Mirror Equation
Refraction At Spherical Surfaces
Ray Diagrams For Lenses
Thin Lens And Lens Maker Equations

Concept #1: Ray Diagrams for Converging Lenses

Transcript

Hey guys, now what we're going to talk about are ray diagrams for converging lenses we talked about ray diagrams for converging mirrors but a mirror's job is to reflect light and produce an image in front of it a lens's is job is to transmit light and produce an image behind it so we're going to see how that works now conceptually with ray diagrams all right let's get to it.When light strikes the surface of a mirror it reflects right this is already something we talked about a bunch but when light strikes the surface of a lens it transmits, lenses are going to be made of transparent material that allows the passage of light through it the transmitted light undergoes refraction just like the reflected light off of a mirror obeys the law of reflection converging lenses right as the name applies are lenses that allow the convergence of light when you have initially collimated light like you do here when it passes through the lens those light rays all bend towards the central axis and therefore they converge on a point this is a point of convergence.The point on the opposite side of the lens where the light converges is known as what guys we know it as the focus.Same as we had for mirrors the thing about lenses though is that in order to draw ray diagrams properly we have to represent focuses on both sides of the lens so whatever this focal length is F, we're going to have a second focus that same distance F on the front side of the lens as well it's just a tool that we need to use in order to draw ray diagram properly. The most common type of converging lens and the one shown in the figure above is called a biconvex lens right it's biconvex because both sides are convex surfaces and it looks convex either way you look at it you could rotate this lens and it's going to look convex no matter how you look at it . Just like with mirrors we can draw ray diagrams to find information qualitative information about the images formed by lenses but we need an associated set of rules for lenses just like we had a set of rules for mirrors so those rules are going to be presented here to draw ray diagrams for converging lenses you need to draw two of the following lines just like the same thing for mirrors a line parallel to the central axis then through the lens towards the far focus. By that I mean the focus on the other side of the lens. Second aligned through the near focus the focus on the side of the lens of the objects then through the lens parallel to central axis and lastly aligned to the very center of the lens that passes through undeflected, that line will not get refracted it's going to pass through the exact same angle and let's do an example to illustrate this process. Draw the image location for the following converging lens is the image upright or inverted and in order to draw ray diagrams you need some sort of ruler or some sort of straight edged object what I have is my trusty protractor because that's what I'm using instead of a ruler now we're going to draw two of the lines and find where they intersect we could draw the third line and it would intersect where the other two do as well all we need to know is where the image is located is to find a point where the two lines intersect so the first line I'm going to draw is parallel to the central axis and for ray diagrams you always draw them to the center of the lens these types of lenses that we're going to be dealing with are called thin lenses which means that compared to the radius of curvature of the lens, they are very very thin so they're essentially occupying a central line so you're always going to that center line that I have indicated. Then from the center line through the focus.The next line is going to be from the object through the focus to the center line of the lens and then parallel to the central axis of our lens and lucky there I just barely caught it. So here is a point of convergence because this blue ray. Is just going to continue and right there is clearly the point of convergence now is this image upright or inverted we're going to use the same convention that we used for mirrors if the conversion of light is below the central axis the horizontal axis then it's inverted if it's above the central axis then it's upright this is clearly below the central axis so this image is inverted.Alright and that wraps up our talk on ray diagrams for converging lenses. Thanks for watching guys.

Practice: If an object is placed within the focus of a converging lens (it’s at a distance of less than the focal length), will a real image form? If so, does it form at a distance less than or greater than the focal length?

Concept #2: Ray Diagrams for Diverging Lenses

Transcript

Hey guys, in this video we're going to talk about ray diagrams for diverging lenses we just took a look at ray diagrams for converging lenses so we know that these should be similar but since the light diverges we know ahead of time some things about the images that are going to be formed alright let's get to it. A diverging lens will never focus light ever because when light rays pass through it they spread further apart they don't come closer together so they will only produce virtual images. I have a picture here of initially collimated light passing through a diverging lens and what it turns out to happen is that if you were to look at the diverging light after it had passed through the lens it all appears to have come up from a point so we have an apparent convergence. This is almost identical to convex mirrors except mirrors reflect light and lenses transmit light.Remember just like with those convex mirrors the light appears to focus on a point which we call the apparent focus for good reason.Though often times we'll just refer to it as a focus because physicists tend to be lazy now because light can pass through either side we need to have a focus that exists on either side of the lens just like we did for converging lenses this is also important in how we're going to draw our ray diagrams alright the most common type of diverging lens is the one shown above which is called the biconcave lens its biconcave because it's a concave surface, either way, you look at it if you were to flip this lens it would still look concave. Just like with mirrors we can draw ray diagrams for these lenses to find out information about the images we did it for converging lenses now we want to do it for diverging lenses and the rules are going to be very similar with slight differences. To draw ray diagrams for diverging lenses you need to draw two of the following lines a line parallel to the central axis then through the lens away from the near focus. Second a line towards the far focus the focus on the other side of the lens then through the lens and parallel to the central axis. Alright and lastly just like for converging lenses a line through the centre of the lens that passes through undeflected.Those are going to be our three rays that we're going to draw we only need to draw two of them to find an intersection of light but those are going to be the three possible rays we can draw for Ray diagrams of diverging lenses. Let's do an example draw the image location for this, this should say diverging lens. Is the image upright or inverted? So before we even begin is the image going to be upright or inverted what do you guys think? This is a diverging lens. So the only images it can produce are virtual images and virtual images are always upright so before we do a single thing we know just the rationalization in our physics knowledge that this image is going to have to be upright I don't have to draw a single line the question was is the image upright you'd be done but where is the image located for that we need to draw ray diagram so the first ray is going to be from the object parallel to the central axis. Right to the center of the lens that's where we always draw and then away from the near lens so I'm drawing it on a line parallel to the near lens but away from it and then I'm going to trace the line back to the origin the apparent origin of that line because that's where your brain is going to see that line coming from next what I need to do is draw a line towards the far focus. But once it hits the center of the lens then it becomes parallel to the central axis and where does this line appear to come from I need to trace it backwards It appears to come from this direction so you can see right there there is an apparent convergence.That is our virtual image and because it's above the horizontal axis because it's above the central axis we know that it's up right exactly as we had predicted alright guys that wraps up our discussion on ray diagrams for diverging lenses. Thanks for watching.

Practice: If an object is placed within the focus of a diverging lens (it’s at a distance of less than the focal length), where will the image form? If so, does it form at a distance less than or greater than the focal length?