Practice: Will an image be formed for an object placed inside the focus of a concave mirror? If so, where will it be formed?
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Concept #1: Ray Diagrams for Concave Mirrors
Hey guys, in this video we're going to talk about Ray diagrams for concave mirrors OK let's get to it. You can see what happens to light when it reflects off of a mirror by drawing what we refer to as Ray diagrams, Ray diagrams are diagrams that simply follow the law of reflection which we've talked about before to show the path of these light rays as they reflect off the surface of these mirrors OK before you can draw any ray diagrams there is one important point on a ray diagram that you always need to find which is known as the focus it's the point where initially collimated light converge's after reflecting off of the mirror so these blue light rays this is light coming in from the left that's collimated remember collimated means all of the light rays are parallel OK this collimated light then encounters the surface of this concave mirror and that causes all of the light to bounce closer towards what we would call the Central Axis.Which goes through the apex. Of our mirror sometimes called the vertex OK. Now this light gets reflected towards the central axis and it converge's on a point right here which we call the focus the point where the light is focused the distance from the apex to this point of focus is known as the focal length and is given by the letter F. Ok now that we know what a focus is when you are given the position of the focus it's very easy to draw Ray diagrams. To draw a diagram for concave mirrors you need to draw two of the following lines OK one is a line parallel to the central axis that when reflected off of the mirror passes through the focus.OK. And that's exactly what we just saw a line parallel to the central axis by definition is reflected through the focus if you draw a line through the focus then it's when it's reflected off the mirror it's parallel to the central axis. OK this is also just geometry If I scroll back up really quickly just like we can follow a line this way and then end up going through the focus if we follow a line through the focus we end up.Reflecting off parallel to the central axis OK it works both ways Lastly if you draw a line to the apex of the mirror it reflects at the same Incidence Angle. And this is just the law of reflection right that if no matter where you are in relation to the mirror you draw the line straight to the apex it bounces off at the same incident angle that's just the law of reflection OK let's see this in action.When light comes off of an object in this case I drew a person a mirror can form an image this is something that we all know right you can look in the mirror, you could look in the spoon any reflective surface and you will see a reflection of yourself that reflection is an image formed by the mirror what we want to talk about is how this image is formed by the mirror OK.And image by definition is a convergence of light in order to find where light converge's we need to draw two lines two of those three possible Ray diagram lines and find the point where they intersect that will be the point where all of the light converge's OK so I'm going to use a protractor because I don't have a ruler and I need to draw these lines straight so just bear with me because this is going to take a moments All right so I have a ray.Coming up off the head of the person and is going to be reflected off of the surface of this mirror.This protractor is not working great for the position that it's in so I'm going to scroll up just a little bit. OK and it hits the surface once it hits the surface it is then reflected through the focus. OK that's the first of our three types of Rays next I'm just going to draw the second one which is through the focus to the edge of the mirror. Straight through the focus to the edge and then parallel to the central axis. Coming off.Well I was worried that it changed at the end OK you can see right here there is a convergence of light OK That convergence of light is going to be an image what is the image of the top of the head of this guy that I drew I want to draw the image of a second part of this guy I want to do it for his hand right.So I'm going to draw the first line which is going to be parallel to the central axis and then through the focus.All right and then I'm going to draw a second ray which is going to go through the focus and then parallel.Something like that OK this is not exact because I'm literally just using a protractor to draw straight lines on the screen in order for ray diagrams to work you would need graphing paper or protractor that you can actually use to find the angles rulers etc but basically what's happening is right here is the image formed of his hand.And right here is the image formed of his head so we can clearly see that the full image of the person is going to be upside down in this case the images inverted OK the central axis for these ray diagrams right this right here provides that information really really easily. If the convergence of the light is below the central axis your image is going to be inverted if the convergence of light is above the central axis your image is going to be upright That way you don't have to look every time at two individual points on an object you can look at one point and see does the light converge above the central axis or below the central axis OK let's do an example. Where would an image be formed for an object at the focal point of a concave mirror so this guy is sitting right on the focal point we can still draw our same lines.Parallel to the central axis then through the focus.OK the second line that I'm going to draw is going to be to the apex ok.The reason is because I can't draw through the focus that would be straight down so I'm going to the third line now and I'm going to draw through sorry to the apex and then.When it comes off the apex it's going to come off at the same angle.That it entered something like this OK now look those two rays don't converge anywhere in this image so clearly if they converge it's going to be way way way behind the guy I want to see if they actually do ever converge in order to test that I have to compare these two angles.Right if theta is larger than Phi that means the blue line will be moving towards the red line and they'll converge eventually. But if Phi is the bigger angle that means the red line is always moving away from the blue line and they never converge so no image will be formed in order to test this or in order to find the relationship between those angles I'm going to draw this as 1 triangle.And I'm going to draw this as another triangle.OK let me minimize myself for this first of all this angle right here is phi right that's the whole point of that third line whatever the incidence angle is that's the same as the reflected angle so this is Phi.But notice what's this leg right here that's just F the focal length how tall is this triangle H. What about for the blue triangle How tall is it H. However Tall the guy is what's this edge length also the focal length look at this these two triangles are identical so theta equals Phi This means no convergence no intersection of the light anywhere which means no image is formed OK so if you have an object on the focal point for a concave mirror no image will ever be formed because the lines coming off the mirror the rays coming off the mirror will always be parallel these two angles are going to be equal and those rays will always be parallel so no image Alright guys that wraps this up thanks for watching.
Practice: Will an image be formed for an object placed inside the focus of a concave mirror? If so, where will it be formed?
Concept #2: Ray Diagrams for Convex Mirrors
Hey guys, in this video we're going to talk about Ray diagrams for convex mirrors we already saw them for concave mirrors now we want to see what they look like for the opposite shaped mirrors All right let's get to it.While a concave mirror converges light as we saw when initially collimated light enters a concave mirror it all comes closer together a convex mirror will diverge light when light reflects off of a convex mirror it spreads apart it doesn't come closer together that means that the light will never focus OK I cannot emphasize this enough off of a convex mirror you will never ever get convergence of light it will always be divergence However if you were looking at this light because your brain is stupid For some reason you only see lines you only see light that's traveling in a straight line so to your brains this line this ray and this ray and this ray this ray this ray and this ray all appear to have come from a point where they focused. This is known as an apparent focus there is an apparent focusing of light or an apparent convergence and your brain cannot tell the difference . So when you look at light coming off of this convex mirror it appears to have focused at this point . This focus while it's not real is often simply referred to as the focus anyway even though it's technically an apparent focus and we can define a focal length just like we did before which is the distance from the Apex to the apparent focus OK. Now to draw Ray diagrams for convex mirrors once again you need to draw two of the three lines these rules are basically the same but slightly different because the focus is on the other side of the mirror so a line drawn parallel to the axis is then reflected off of the mirror away From the focus.A line towards the focus is then reflected off of the mirror parallel to the central axis And finally a line to the apex of the mirror is reflected at the same Incidence angle. So the third line is the same the third rule for Ray diagrams is the same the first two are very similar but slightly different in how you apply them because the focus is on the opposite side of the mirror let's see what I mean I'm going to minimize myself so we have an unobstructed view of this image.When light comes off of an object a convex mirror can also form an image which is what we're about to see OK I cannot stress this enough though this image is not actually a real image it's not real because light never converges Let's see what I mean by this I'm going to draw the first type of ray which is going to be parallel to the central axis and then reflected off of the Mirror. In the direction away from the focus so you see that green line. The reflected Ray follows that green line as if it was leaving the focus now the second line goes towards the focus if I were to continue this.It would look like it was going towards the focus I don't want to have that right now but that's what I mean by towards the focus and then it's reflected off of the mirror parallel to the central axis.But notice something, when you see this Ray it appears to have come straight across from the other side of the mirror right so there appears to be a focus there is an apparent image.This image is not real this image is not there because the light never actually converges there but it sure does appear to our brains like it's there now I'm going to draw how we always draw images as just being an arrow that points from the central axis to the focus so this would be up right because it's above the horizontal axis OK since this light appears to converge to our brains this looks identical to any other image this is known as a virtual image or an apparent image it's not real it's just virtual And in this case the images is up right. Right the apparent focus point the apparent convergence of light occurs above the central axis so the image is up right but these images are not real they are virtual images but to our eyes they appear to be real. OK let's do a quick example. Where would the image be formed for an object of focal length away from the surface of a convex mirror so I'm just going to use the first ray diagram the first ray which is parallel to the central axis and then directed away from the focus. Whenever you are drawing these lines you need to continue them.On the other side like this so you know where the light appears to have intersected. The second one is towards the focus and then off of the mirror parallel to the central axis so that's towards the focus and then off of the mirror parallel to the central axis I need to complete this.So you see right here we have an apparent convergence of light which is known as.A virtual image and it will appear inside of the focus of the convex mirror ok. That wraps up this discussion on ray diagrams for convex mirrors Thanks for watching guys.
Practice: Find the location of the virtual image produced by a convex mirror when the object is placed a distance less than the focal length form the surface of the mirror.
Concept #3: Ray Diagrams for Plane Mirrors
Hey guys, so far we've done convex mirrors and we've done concave mirrors but now the final type of mirror plane mirrors Not plain as in simple but P L A N E plane as in flat these are the types of mirrors that you would hang on your wall these are your bathroom mirrors etc So by far the most popular kind of mirror all right let's get to it.Collimated light coming off of a plane mirror doesn't converge or diverge right the law of reflection says that if you're hitting a flat surface perpendiculars that surface you bounce off at the same angle right so all the blue rays those initially collimated rays of light all bounce off collimated.The light doesn't converge or diverge that means that there's no focus for a plane mirror not on the front side of it and not an apparent focus on the back side of it sometimes just for equations which we'll cover in the future just to make those equations work the focal length of a plane mirror is said to be infinity.It's said that infinitely far away hypothetically those lines could converge it's just a mathematical tool to make equations that we'll see in a little bit work better. To draw rays diagrams for plane mirrors we need to draw two of the following lines there are two types of line but the second line is actually an infinite number and I'll get to that in a second number one aligned parallel to the central axis then reflected off of the mirror parallel to the central axis.Right and that's exactly what I showed in the image above if you come in parallel to the central axis you leave parallel to the central axis and then any line. From anywhere to any point on the mirror that's reflected at the same incidence angle. For convex and concave mirrors the second point was only true for lines that went to the apex but for plane mirrors because they're flat everywhere not just at the apex this applies to any line drawn at any point on the surface let's do an example.A 1.6 meter tall person stands 0.7 meters away from a plane mirror how tall does the person appear in the mirror how far from them mirror does the image appear is this image real or virtual. So just a whole bunch of information about the image that they want to know so let's draw our lines .First parallel and this is going to return parallel so this one is a rounded trip it goes both ways but this also means though.Is when it's coming back to you it appears as if it came off the other side of the mirror, parallel right. Now what I'm going to do next is I'm going to draw a line from the head to half way down the body because then it's going to reflect at a 45 degree angle and reach the feet so from the head I can choose any point on the mirror and it will reflect at the same angle that it hits but I'm strategically choosing. To have it reflect at a point halfway down the person's body and so I need to draw where this line appears to come from and you can see right away there is an apparent convergence of light so there is an image here right. What type of image is it a real image or is it a virtual image this is absolutely a virtual image.This is not real because light is not actually converging on that point it only appears to converge on that point. Furthermore the only types of mirrors that can produce real images are mirrors that can actually converge light which are concave mirrors convex mirrors diverge light so they can never form a real image and plane mirrors don't converge or diverge but since they don't converge they cannot form a real image either what's the height of this image well look at this particular green line it's at the same height as the person so the height of the image is just 1.6 meters now the question is how far away is this? well this angle, is actually going to be the same as this angle. These two triangles are identical triangles that means that this distance has to be the same. So you're going to find that whenever an object is in front of a plane mirror that mirror produces a virtual image of the same height as the object upright and the same distance behind the mirror that the object exists in front of the mirror. This wraps up our discussion on Ray diagrams for plane mirrors Thanks for watching guys.
Practice: You want to hang a plane mirror on your wall. If you want your entire body to fit into the mirror, what’s the maximum height off the ground that the mirror must be? What is the smallest mirror you can buy? Consider yourself to be 1.55 m tall.
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