okay Premed let's talk mirrors and lenses Optics questions can be really tricky on the mcap because there are a lot of specific terms definitions and finicky relationships that you need to learn today I'm going to walk you through my personal lenses and mirrors study guide and we're going to build it together step by step all right so we've just got a blank page here we're going to zoom in and draw all the details about lenses and mirrors that you'll need to know for teste we're going to start with mirrors now mirrors is an area that's less likely to show up on test stay still important to contrast with lenses but just know that you'll get less questions on them so maybe Focus A Little Less in your prep all right so we're going to start with mirrors off to the left so mirrors reflect light right they do not refract it any light rays that come in bounce right back off so here's my light rate coming in and they're just going to bounce off reflect right back the way they came now depending on the shape of the mirror the curve of the mirror you are going to get two different types of bouncing or reflecting so for our mirror on the left here which is known as a concave mirror in terms of shape right so we're going to draw this we're going to draw everything concave in purple all right so concave is in terms of shape is also what's known as a converging system all right converging system that means that when light comes in to a concave mirror like so the light rays are going to converge as they reflect they're going to come in towards each other as they reflect to a focal point so that is a converging concave mirror now the other type of mirror we're going to draw in green is a convex mirror concave because it looks like a cave convex right kind of belly shaped and a convex Mirror Has diverging Rays diverging meaning they separate as they reflect so again rays are coming in and in a diverging mirror or diverging system those light rays are going to go further away from each other as they reflect now when we get to lenses in a moment I want you to see that these terms do not line up exactly with lenses so concave converging mirrors convex diverging mirrors it's going to be different for our lenses so concave and convex describe the shape shape and diverging and converging describe the Rays right the light rays all right now other things to know about mirrors um again they're less likely to be tested but still may come up with some math so we're going to just draw little mirror system here we'll go ahead and draw a concave mirror like so all mirrors and lenses have a focal length this is a characteristic of the mirror and the lens so there's no consistent focal length right it's going to be specific to this specific mirror um and so they'll give it to you in a question if they want you to calculate it or you'll ask to solve for it with the equations that we're going to go through for a mirror there's also something called the center of curvature or C the center of curvature to the center of the mirror is known as the radius of curvature right if we were to draw the mirror as a full circle right radius of curvature and our calculations here that are relevant for Mirror are that 2 r r meaning the radius of curvature is equal to 1 over focal length all right so 2 Ral 1 over focal length or 1/2 focal length equals R we're going to get back to these two equations after we finish talking about our lenses all right so that's mirrors now let's go over to our lens's side of our notes unlike mirrors in a lens light is going all the way through and refracting through the other side so in a lens our shape either looks like this which is a convex shape right imagine two convex mirrors put together right that kind of belly shape and we have diverging mirrors I'll have to draw these versus draw a little shape this is a concave lens which are very much like two concave mirrors pushed together right so this is again describing the shape of the lens now here's the part where it gets a little tricky unlike mirrors a convex lens is a converging system so see how they're kind of flipped so in this case because the light rays are going through through they're kind of kind of Uno reversing and we end up converging on the other side of the lens in contrast the concave lens is a diverging diverging ing lens where when the Rays come in they actually diverge away from each other now for both a convex in a concave system the image is formed on the other side of the lens versus being reflected back on the same side as the object so when we draw the system I'll go ahead and draw a converging system here and a diverging system here we have our object which is usually upright and we have a focal length so this is our object object we have our focal length again this is a characteristic of the lens it's on both sides we have focal length focal length most of the time the focal length is smaller than the object distance that's what we're drawing here where the image is formed and in which direction inverted or upright depends on the relationship between the focal length the object distance and the characteristics of the lenses so now let's get into some rules by definition a converging lens has a focal length that is positive all right so it's going to be a positive value just a characteristic of the lens because it's a converging lens a diverging lens right or concave lens by definition will have a focal length that is negative again characteristic of the lens now the D for both systems is going to be positive pretty much all the time on MCAT question so our object distance which is our distance between between our object and the center of our lens d o is going to be positive so now we can actually determine whether our image distance is positive or negative by using the thin lens equation so let's go ahead to the center here because the thin lens equation can actually be used for mirrors too uh just tends to not be so let's go ahead to the center so we can put the thin lens equation right in the center here so our thin lens equation is 1/ f = 1/ d o + 1/ di it's a reciprocal equation and now I'm going to tell you these rules you can trust me on it or you can do the math to prove it because our focal length is positive here and our do is positive here as long as D is greater than the focal length as long as our distance of our object is greater than our focal length di will be positive for a converging lens and again you can do that math to try it out with the thin lens equation to prove it but this is always going to be trick for our diverging lens it's going to be the opposite relationship as long as D is greater than F di will be negative because of our negative focal length all right as long as again D is greater than F so why do we care whether the image distance is positive or a negative value because that value and the magnitude of the image distance lets us know important things about what images formed like whether it's real or virtual or upright or inverted or enlarged or reduced we can determine all of that from the sign value of the image distance and we can use nice shortcuts and tricks to do this without having to do calculations every time before we get into all that I'm Amanda Bram and I've been coaching students through their MCAT Journeys since 2019 please remember to subscribe to this channel for more videos on MCAT content test taking strategies and mental fitness tips that will help you perform your best on testing and if you'd like more interactive in-depth lessons on topics like these please check out the link in the caption below which will take you to register for my next MCAT course all right let's finish out this study guide with what types of images are formed with which type of lens so here's our first set of rules if di is positive POS this is a real image all right real and virtuals are just terms that we use to describe the types of images that are formed for a positive image distance that means it's a real image for a negative distance image that's a virtual image so by definition our convex converging lens produces real images and our diverging lens by definition produces virtual images now to get to our next set of characteristics we need one more equation we need our magnification equation magnification is equal to di over D so magnification how big or how small something is and it's equal to negative the image distance over the object distance so that's our equation now let's get into our rules if the magnific is positive then the image is upright if the magnification is negative then the image is inverted so check it out if we have a negative di like we have here a negative time a negative is a positive so we're going to have an upright image so our diverging lens produces a virtual upright image and it will always form a virtual upright image because in order for it to be upright the DI needs to be negative which means it needs to be virtual so here's your first pneumonic UV goes together like UV light all right so u and v go together if it's upright it's got to be virtual and vice versa and both of those apply to a diverging or concave lens now for our converging lens we can see that we have a positive di which if we plug into our equation here would give us a negative value and so therefore will have an inverted image so real images always also are inverted images which again we can use a pneumonic I like infrared light so IR goes together and UV goes together it will always be true on MCAT style questions finally if the absolute value so it doesn't matter positive or negative if the absolute value of M is greater than one the image is enlarged and this should make sense conceptually because our distances are proportional to our Heights so if our image distance is bigger than our object distance we're going to get a value of greater than one which also means that we're going to get an image that is bigger than our object so if our absolute value of the magnification is greater than one that just means hey our image distance is bigger than our object distance therefore our image itself is bigger than our object object on the other side if our absolute value of M is less than one it's going to be reduced and again that's because our Heights of our images and our objects are proportional to our distances so our final equation here we're going to write off in the corner is the ratio of the heights hi image height over ho object height is equal to the distance of the image over the distance of the object all this means conceptually is that if you're further away from the lens you're also going to be taller all right so the further away you are in distance from the lens the taller our object are our images and it's proportional all right it's directly proportional the bigger the distance of the object the bigger the distance of the image the bigger the height of the image the pneumonic for this equation is hi ho Dao all right so it's an easyish one to remember hi ho da do and just know that our Heights are proportional to our distances again as a reminder here are our mirror equations with our radius of curvature that is only used for mirrors however we can substitute in this equation to our thin lens equation thin lens equation tle up here as well all right and as you can see we now have our finished study guide notice there's not a lot of words or explanations here that's because it is so important to use the study guide as a trigger to to get you to think through the concepts that we just talked about in this video please feel free to watch it again try to draw it from memory until these concepts are locked down and you're ready to move on to math problems all right I hope you enjoyed that walkthrough of mirrors and lenses on the MCAT if you found this video helpful please share it with your Premed Community remember studying for the MCAT can be hard and stressful and sometimes we all need a little help thanks so much and happy studying