Chapter 13: Mirrors and Lenses Section 1 : Mirrors Section 2: Lenses Section 3: Optical Instruments

Section 1 : Mirrors Plane mirrors A mirror with a flat, smooth surface  Your reflection in a plane mirror is what another person would see if he/she looked at you How the mirror works:  Light rays travel from the source to you  Every point struck by the light reflects the waves so that they travel outward in all directions  The reflected rays strike the mirror and are reflect back to you Virtual images  Remember, your brain always interprets light rays as if they have traveled in a straight line  Doesn’t recognize if the rays are reflected or refracted  If the reflected rays were extended behind the mirror they would meet at a single point  Your brain thinks that the rays that enter your eyes are coming from this point, and seem to see your reflection at this point (your reflections seems to come from behind the mirror)  The reflected image is a virtual image  Light rays diverge and do not pass through you

Section 1 : Mirrors Concave mirrors The surface of the mirror curves inward Principal axis (aka optical axis) - an imaginary line drawn perpendicular to the surface of the mirror at its center Focal point – point on the principal axis through which the reflected rays of rays drawn parallel to the principal axis pass  If a light ray passes through the focal point and then strikes the mirror, the reflected ray will be parallel to the principal axis Center of curvature – an imaginary point on the principal axis that marks the center of the circle that would be formed if the ends of the mirror were extended.  If a light ray passes through the center of curvature, the reflected ray will pass through the focal point Focal distance – the distance from the center of the mirror to the focal point is the F C principal axis F = focal point; C = center of curvature object image

Section 1 : Mirrors Concave mirrors The location of an object relative to the focal point (F) and the center of curvature (C) determines the type of image that will be formed by the light reflected from the mirror: 1.Object infinite distance from a concave mirror - reflected rays all pass through the focal point, and no image is formed 2.Object a finite distance beyond center of curvature - image formed is real, inverted, reduced, and located between C and F 3.Object located on center of curvature - image formed is real, inverted, same size as the object, and located at C 4.Object between C and F - image is real, inverted, enlarged, and located behind C 5.Object is on the focal point - rays are reflected parallel to each other, no image is formed 6.Object is between F and the mirror - image is virtual, upright, enlarged, and located behind the mirror

Section 1 : Mirrors Convex mirrors The surface of the mirror curves outward  The image formed is virtual, upright, reduced, and located behind the mirror between the mirror and the focal point principal axis F C image

Section 2: Lenses A lens is a transparent material with at least one curved surface the causes light rays to refract as they pass through There are two types of lenses  Concave – a lens that is thicker at the edges than in the center  Convex – a lens that is thicker in the center than at the edges

Section 2: Lenses The image formed by light passing through a convex lens is relative the location of the object when referenced by two points located on the principal axis located at 1 focal length (F) and two focal lengths (2F) 1.Object an infinite direction from lens - The rays are parallel to the principal axis and the image formed is a point at the real focus 2.Object at a finite distance beyond 2F’ - Image is real, inverted, reduced and located between F and 2F 3.Object at a distance equal to 2F’ - Image is real, inverted, the same size as the object, and located at 2F 4.Object at a distance between F’ and 2F’ - Image is real, inverted, enlarged, and located beyond 2F 5.Object is at a distance of F’ - The rays are parallel to each other as they leave the lens no image is formed 6.Object at a distance between F’ and the lens - Image is virtual, upright, enlarged, and located between 2F’ and F’ F F’ 2F 2F’ object image

Section 2: Lenses Concave lens Also called a divergent lens because light rays diverge as they pass through the lens  The only image formed is virtual, upright, reduced, and located between F’ and the lens FF’ object image

Section 2: Lenses Lenses and eyesight The structure of the eye gives you the ability to focus on objects around you  In a normal eye, light travels through the cornea to the convex shaped lens  The waves converge on the focal point on the retina where they are converted into electrical impulses and sent to the brain via the optic nerve  In order to focus on objects, the lens in your eyes must be flexible so the focal length changes  Muscles control the shape of the lens  When focusing on distant objects, the muscles stretch the lens making it less convex and increasing the focal length  When focusing on close objects, the muscles make the lens more convex and so decreasing the focal length  Your eyes lose this focusing ability when you are around 50 years old

Section 2: Lenses Vision problems Farsightedness – can see distant objects clearly but cannot focus on nearby objects  Eyeball is too short, the focal point is behind the retina – a convex (converging lens) lens will correct this problem Nearsightedness – can see close objects clearly, but cannot focus on distant objects  Eyeball is too long, the focal point is in front of the retina – a concave (diverging) lens will correct this problem Astigmatism – the surface of the cornea is curved unevenly  Causes blurry vision at all distances  Corrective lenses will be curved to cancel this unevenness

Calculations for Mirrors and Lenses The lens/mirror equation There is a relationship between the focal length or the lens or mirror and the object and image distances Example: What is the focal length or the object is 10-cm from the lens and the image formed is 12-cm? Solution You can also solve for d o and d i The equation:Where: f = focal length d o = object distance d i = image distance

Calculations for Mirrors and Lenses Magnification Magnification is the ratio of the size (height) of the image to the size (height) of the object, or: Example: If the object is 56-cm high, and the image formed is 20-cm, what is the magnification? Solution Notice that the distance units cancel, magnification is just a number. Where:M = magnification h i = image height h o = object height h o = 5.0 cm h i = 20.0 cm M = ?

Calculations for Mirrors and Lenses Where:S i = image size S o = object size d i = image distance d o = object distance