Transcript for:
Exploring Reflection and Lens Formation

Hi there! In the previous lessons, we learned about the different regions of the electromagnetic spectrum. If you can recall, one of those regions is visible light. If you still haven't watched the previous lessons, you can pause this video and watch that one. one first to better understand our lesson today. What do you see when you look at a mirror? How do you compare the way you look and the way your image looks? Can you explain how your image is formed on the mirror? This new lesson will help answer these questions. Reflection is the bouncing of light rays when it hits a surface like a plain mirror. Plain mirrors exhibit regular or specular reflection where the angle of incidence is equal to the angle of reflection. Specular reflection is reflection of smooth surfaces. All plain, shiny surfaces exhibit this kind of reflection. On the other hand, irregular or diffuse reflection illuminates shaded areas such as under the trees and inside buildings. Diffuse reflection is reflection of rough surfaces. This is observed in objects with irregular surfaces, such as rocks and buildings. The law of reflection states that the angle of incidence is equal to the angle of reflection. The angle of incidence is measured between the normal line and the incident ray, while the angle of reflection is measured between the normal line and the reflected ray. Before we proceed, let us first define some terms. The resulting reflected image can be characterized according to image, orientation, location, size, and magnification. Magnification is the ratio of the image dimensions to the object dimensions. An image may be real or virtual. The main difference between real and virtual images lies in the way in which they are produced. A real image is formed when rays converge, whereas a virtual image is shown when rays only appear to diverge. An image's orientation can be upright if it is right-side up and inverted if it is upside down. The location of the image always depends on the location of the object. The size may be larger, smaller, or the same with a magnification of greater than 1, lesser than 1, or equal to 1 respectively. Now we're all set! Imagine yourself looking at a bee above you in the mirror. For plain mirrors, the type of image is virtual and is formed from behind. The image orientation is upright and laterally inverted. The image is located at the same distance from the mirror as the object's distance and the image formed is of the same size as the object. Plane mirrors produce images that have a magnification of 1. In other words, the image and the object in plane mirrors have the same characteristics, except that the image is seen as laterally inverted. So what is lateral inversion? Lateral inversion is a phenomenon wherein the left side of the object appears to be on the right side of the reflected image. and vice versa. This is due to the direction that light follows when it strikes a reflecting surface, generally like a mirror. This is the reason why the word ambulance is written in a reverse manner in front of the ambulance van so it can be read easily. Try looking at your image on both sides of a spoon. What have you noticed? This is a reflection on curved mirrors. A curved mirror is a reflecting surface that is a section of a sphere. There are two kinds of curved mirrors, convex and concave. A spoon is a kind of curved mirror with a concave side and a convex side. Concave mirrors can be seen on the inside of the sphere and convex mirrors can be seen on the outside of the sphere. A line passing through the exact center of a concave mirror is known as the principal axis. The point in the center of the sphere from which the mirror was sliced is known as the center of curvature and is denoted by the letter C. The point on the mirror's surface where the principal axis meets the mirror is known as the vertex and is denoted by the letter A. The vertex is the geometric center of the mirror. Midway between the vertex and the center of curvature is a point known as the focal point denoted by the letter F. When the object is located at a location beyond the center of curvature, the image will always be located somewhere in between the center of curvature and the focal point, regardless of exactly where the object is located. the image will be located in the specified region. In this case, the image will be an inverted image and is reduced in size. In other words, the image dimensions are smaller than the object dimensions. If the object is a 6-foot tall person, then the image is less than 6 feet tall. The absolute value of the magnification is less than 1. and the image can be described as a real image. When the object is located at the center of curvature, the image will also be located at the center of curvature. In this case, the image will be inverted. The image dimensions are equal to the object dimensions. A 6-foot tall person would have an image that is 6 feet tall. and the absolute value of the magnification is equal to 1. The image produced is a real image. Light rays actually converge at the image location. Regardless of exactly where the object is located between the center of curvature and focal point, the image will be located somewhere beyond the center of curvature. In this case, the image will be inverted. The image dimensions are larger than the object dimensions. A 6-foot tall person would have an image that is larger than 6 feet tall, and the absolute value of the magnification is greater than 1. The image formed is a real image. When the object is located at the focal point, no image is formed. Light rays from the same point on the object will reflect off the mirror and neither converge nor diverge. After reflecting, the light rays travel parallel to each other and do not result in the formation of an image. When the object is located at a location beyond the focal point, the image will always be located somewhere on the opposite side of the mirror. In this case, the image will be an upright image. The image is magnified or in other words, the image dimensions are greater than the object dimensions. A 6 foot tall person is a 6 foot tall person. person would have an image that is larger than 6 feet tall and the magnification is greater than 1. Light rays from the same point on the object reflect off the mirror and diverge upon reflection. For this reason, the image location can only be found by extending the reflected rays backwards beyond the mirror. The point of their intersection is the virtual image location. It would appear to any observer as though light from the object were diverging from this location. In convex mirrors, the location of the object does not affect the characteristics of the image. Convex mirrors will always produce a virtual, upright, and smaller image located on the opposite side of the mirror. Unlike concave mirrors, convex mirrors always produce images that share these characteristics. As such, the characteristics of the images formed by convex mirrors are easily predictable. Now let us determine the characteristics of the images formed by curved mirrors using the mirror equation 1 over F equals 1 over P plus 1 over Q where F is the focal length or the distance from the mirror and the focal point. P is the distance of the object from the mirror and Q is the distance of the image from the mirror. We also use the magnification equation h with an apostrophe over h equals negative Q over P. Now remember, focal length is positive if the mirror is concave and negative if it is convex. The distance of the image from the mirror is positive if the image is real and located in front of the mirror and it is negative if the image is virtual and located behind the mirror. H with an apostrophe is the height of the image. It is positive if the image is upright and negative if the image is inverted. Let's try some sample problems. A 5 cm tall light bulb is placed at a distance of 45 cm from a concave mirror having a focal length of 10.5 cm. Determine the image distance and the image size. The given values in the problem are the height of the object, which is 5 cm, distance of the object, which is 45 cm, and focal point. which is 10.5 cm. We are going to find the distance of the image or Q and the height of the image or H with apostrophe. The formula is 1 over focal point equals 1 over distance of the object plus 1 over distance of the image. Now let's replace the given values. We have 1 over 10.5 cm equals 1 over 45 centimeters plus 1 over distance of the image. First, let's subtract both sides by 1 over 45 centimeters to cancel the 1 over 45 centimeters on the right side of the equation. After subtracting both sides by 1 over 45 centimeters, we have a new equation. 1 over 10.5 centimeters minus 1 over 45 centimeters equals 1 over distance of the image. In subtracting fractions, you need to have the same denominator, or the lower number. To have the same denominator, multiply both fractions with the denominator of the other fraction. So, 1 times 45 and 10.5 times 45 equals 45 over 472. 1 times 10.5 and 45 times 10.5 equals 10.5 over 472.5 cm. Now we have the new equation, 45 over 472.5 cm minus 10.5 over 472.5 cm equals 1. Over distance of the image 45 over 472.5 minus 10.5 over 472.5 equals 34.5 over 472.5. Next, we cross multiply both sides of the equation to make this equation into a whole number, not a fraction. Now we have the equation 34.5Q equals 472.5 centimeters. Lastly, to get the Q. or distance of the image from the mirror, we divide both sides by 34.5. We can cancel out the 34.5 on the left side, which leaves us with only Q. 472.5 centimeters divided by 34.5 equals 13.7 centimeters, which is the distance of the image from the mirror. Next, The image height can be determined using the magnification equation. Height of the image over height of the object equals negative distance of the image over distance of the object. We already have the value for the distance of the image. Since three of the four quantities in the equation are known, the fourth quantity can be calculated. The equation will now be height of the image over 5 centimeters. equals negative 13.7 centimeters over 45 centimeters. Again, we cross multiply both sides of the equation to make this equation into a whole number, not a fraction. We have the equation 45 centimeters times height of the image equals 13.7 centimeters times 5 centimeters. which is equal to 68.5 cm2. We divide both sides by 45 cm to cancel out 45 cm on the left side of the equation, which leaves us only the height of the image. Negative 68.5 cm2 divided by 45 cm equals negative 1.5 cm. We cancel out the square since we are dividing. Height of the image is equal to negative 1.5 centimeters. Take note, a negative value for image height indicates an inverted image. Alright, so that's it for mirrors. Now let's proceed to lenses. A lens is merely a carefully ground or molded piece of transparent material that refracts light rays in such a way that it forms an image. A convex lens is a lens that converges rays of light that are traveling parallel to its principal axis. Converging lenses can be identified by their shape. They are relatively thick across their middle and thin at their upper and lower edges. A concave lens is a lens that diverges rays of light that are traveling parallel to its principal axis. Diverging lenses can also be identified by their shape. They are relatively thin across their middle and thick at their upper and lower edges. A line passing through the exact center of the lens is known as the principal axis. A lens also has an imaginary vertical axis that bisects the symmetrical lens into halves. As mentioned earlier, light rays that incident towards either face of the lens and traveling parallel to the principal axis will either converge or diverge. For convex lenses, the point where light converges is called the focal point. The focal point is denoted by the letter F. Technically, a lens does not have a center of curvature. However, a lens does have an imaginary point that we refer to as 2F point. This is the point on the principal axis that is twice as far from the vertical axis as the focal point is. If the light rays diverge, as in a concave lens, then the diverging rays can be traced backwards until they intersect at a point. This intersection point is known as the focal point of a concave lens. Note that each lens has two focal points, one on each side of the lens. Unlike mirrors, lenses allow light to pass through either face, depending on where the incident rays are coming from. Subsequently, Each lens has two possible 2F points. When the object is located at a location beyond the 2F point, the image will always be located somewhere in between the 2F point and the focal point on the other side of the lens. Regardless of exactly where the object is located, the image will be located in the specified region. In this case, the image will be an inverted image. The image dimensions are smaller than the object dimensions. If the object is a 6 foot tall person, then the image is less than 6 feet tall. The magnification is a number with an absolute value less than 1. Finally, the image is a real image. When the object is located at the 2F point, the image will also be located at the 2F point on the other side of the lens. In this case, the image will be inverted. The image dimensions are equal to the object dimensions. A 6-foot tall person would have an image that is 6 feet tall. The absolute value of the magnification is exactly 1. Also, the image is a real image. When the object is located in front of the 2F point, the image will be located beyond the 2F point. on the other side of the lens. In this case, the image will be inverted. The image dimensions are larger than the object dimensions. A six foot tall person would have an image that is larger than six feet tall. The absolute value of the magnification is greater than one. The image is a real image. When the object is located at the focal point, no image is formed. The refracted rays neither converge nor diverge. After refracting, the light rays are traveling parallel to each other and cannot produce an image. When the object is located at a location in front of the focal point, the image will always be located somewhere on the same side of the lens as the object. The image is located behind the object. In this case, the image will be an upright image. and the image is enlarged. A 6-foot tall person would have an image that is larger than 6 feet tall. The magnification is greater than 1. Finally, the image is a virtual image. Light rays diverge upon refraction. For this reason, the image location can only be found by extending the refracted rays backwards on the object's side of the lens. In concave lenses, the location of the object does not affect the characteristics of the image. The resulting image will always be smaller than the object, with a magnification less than 1. The virtual image will be upright and located on the same side of the object. Unlike convex lenses, concave lenses always produce images that share these characteristics. As such, the characteristics of the images formed by concave lenses are easily predictable. Remember the mirror equation we used earlier? That equation can also be applied to lenses. To recall, F is the focal length and distance of the object from the lens, P is the distance of the object from the lens, Q is the distance of the image from the lens, and lastly, H is the focal length and distance of the object from the lens. with an apostrophe is the height of the image. When the lens equation is used in determining the characteristics of images formed by lenses, we will refer to this sign convention for lenses. Focal length is positive if the lens is double convex, and negative if the lens is double concave. Notice that it is the opposite in mirrors. Distance of the image from the lens is positive if the image is real and located behind the lens, and negative if the image is virtual and located on the object's side of the lens. Take note that the location of the image is also opposite in mirrors. Lastly, the height of the image is positive if the image is upright, and negative if the image is inverted. The steps in solving lens problems are as follows. are the same as those in mirror problems. Here's a quick recap. The law of reflection states that the angle of incidence is equal to the angle of reflection. A plain mirror will always result to the same image characteristics regardless of object location. Image characteristics in concave mirrors depend on the object's location. On the other hand, convex mirrors will always produce the same image characteristics. Image characteristics in convex lenses depend on the object's location while concave lenses will always produce the same image characteristics. That's all for now. We will be discussing about uses of mirrors and lenses in optical devices in our next video so stay tuned. See you on our next video. and don't forget to keep your minds busy! If you like this video, please subscribe to our channel and hit the notification icon for more videos like this!