Optics Mirrors and Lenses

Reflection We describe the path of light as straight-line rays Reflection off a flat surface follows a simple rule: –angle in (incidence) equals angle out (reflection) –angles measured from surface “normal” (perpendicular) normal same angle incident ray reflected ray

Reflection Vocabulary Real Image – –Image is made from “real” light rays that converge at a real focal point so the image is REAL –Can be projected onto a screen because light actually passes through the point where the image appears –Always inverted

Reflection Vocabulary Virtual Image– –“Not Real” because it cannot be projected –Image only seems to be there!

Virtual Images in Plane Mirrors If light energy doesn't flow from the image, the image is "virtual". Rays seem to come from behind the mirror, but, of course, they don't. It is virtually as if the rays were coming from behind the mirror. "Virtually": the same as if As far as the eye-brain system is concerned, the effect is the same as would occur if the mirror were absent and the chess piece were actually located at the spot labeled "virtual image".

Plane (flat) mirrors Plane mirrors produce images that : a. The object distance is equal to the image distance b. Are upright c. The same size d. Virtual Object distance: The straight-line distance d o from the surface of a mirror to the object. Image distance: The straight-line distance d i from the surface of a mirror to the image.

LEFT- RIGHT REVERSAL

Curved mirrors What if the mirror isn’t flat? –light still follows the Law of Reflection – the curve creates the focal point for the light Parabolic mirrors are curved mirrors with exact focus –used in telescopes, backyard satellite dishes, etc. –also forms virtual image

Concave Mirrors Curves inward May be real or virtual image View kacleaveland's map Taken in a place with no name (See more photos or videos here)more photos or videos here "Have you ever approached a giant concave mirror? See your upside-down image suspended in mid-air. Walk through the image to see a new reflection, right-side-up and greatly magnified. In the background you see reflected a room full of visitors enjoying other

For a real object between f and the mirror, a virtual image is formed behind the mirror. The position of the image is found by tracing the reflected rays back behind the mirror to where they meet. The image is upright and larger than the object. For a real object close to the mirror but outside of the center of curvature, the real image is formed between C and f. The image is inverted and smaller than the object. For a real object outside of (beyond) the center of curvature, the real image is formed between C and f. The image is inverted and smaller than the object.

For a real object between f and the mirror, a virtual image is formed behind the mirror. The position of the image is found by tracing the reflected rays back behind the mirror to where they meet. The image is upright and larger than the object. For a real object close to the mirror but outside of the center of curvature, the real image is formed between C and f. The image is inverted and smaller than the object. For a real object between C and f, a real image is formed outside of C. The image is inverted and larger than the object. For a real object at C, the real image is formed at C. The image is inverted and the same size as the object. For a real object at C, the real image is formed at C. The image is inverted and the same size as the object.

For a real object between f and the mirror, a virtual image is formed behind the mirror. The position of the image is found by tracing the reflected rays back behind the mirror to where they meet. The image is upright and larger than the object. For a real object close to the mirror but outside of the center of curvature, the real image is formed between C and f. The image is inverted and smaller than the object. For a real object between C and f, a real image is formed outside of C. The image is inverted and larger than the object. For a real object between C and f, a real image is formed outside of C. The image is inverted and larger than the object.

For a real object between f and the mirror, a virtual image is formed behind the mirror. The image is upright and larger than the object. For a real object between f and the mirror, a virtual image is formed behind the mirror. The position of the image is found by tracing the reflected rays back behind the mirror to where they meet. The image is upright and larger than the object.

For a real object between f and the mirror, a virtual image is formed behind the mirror. The position of the image is found by tracing the reflected rays back behind the mirror to where they meet. The image is upright and larger than the object. For a real object close to the mirror but outside of the center of curvature, the real image is formed between C and f. The image is inverted and smaller than the object. For a real object close to the mirror but outside of the center of curvature, the real image is formed between C and f. The image is inverted and smaller than the object. What size image is formed if the real object is placed at the focal point f? For a real object at f, no image is formed. The reflected rays are parallel and never converge.

Convex Mirrors Curves outward Reduces images Virtual images –Use: Rear view mirrors, store security… CAUTION! Objects are closer than they appear!

Cf Convex Mirror object image For an object placed anywhere in front of a convex mirror, the image is virtual, upright and smaller

Lenses Converging Lens Diverging Lens F F f f

Convex Lenses Thicker in the center than edges. –Lens that converges (brings together) light rays. –Forms real images and virtual images depending on position of the object The Magnifier

Concave Lenses Lenses that are thicker at the edges and thinner in the center. –Diverges light rays –All images are erect and reduced. The De-Magnifier

Find the focal length of a converging lens by holding it up to a window. (See how far away from the lens you need to hold a piece of paper to focus the image on the paper.) W

Ray Tracing for Lenses Light passes through a lens There is a focal point on both sides of a lens Converging Lens: Ray #1: Parallel to the axis Refracts through F Ray #2: Through F Refracts parallel to axis Ray #3: Through Center of lens undeflected

Example: Camera

Example: Slide Projector

How You See Near Sighted – Eyeball is too long and image focuses in front of the retina Far Sighted – Eyeball is too short so image is focused behind the retina.

The Human Eye Web Links: Eye lens,Eye lens Vision and Eyesight Near Point – Closest distance the eye can focus on (about 25 cm when we are young) Far Point – Farthest distance the eye can focus on (should be  )

Someone who is Nearsighted cannot focus on far away objects. Nearsightedness can be corrected with diverging lenses Here’s how it works

Someone who is Farsighted cannot focus on objects too near. Farsightedness can be corrected with converging lenses Here’s how it works

Example: Magnifying Glass Web Link: Ray tracing Ray tracing

Results: Ray Tracing for Converging Lenses (in each case, draw in the 3 rays for practice) Object distance > 2f: Image is real, smaller, and inverted FF2F Object between f and 2f: Image is real, larger, inverted FF2F Object between f and mirror: Image virtual, larger, upright FF2F

Converging Lens: Image Formation F F The image is real and inverted. In this case, the image is about the same size as the object, but the size of the image will depend on the position of the object relative to the focal point of the lens. Make sure you do the ray tracing to figure out the image position and size!

Converging Lens: Image Formation F F The image is still real and inverted. We’ve moved the object closer to the lens, and the image is now magnified (larger than the object).

Converging Lens: Image Formation F F If we move the object very close to the lens (less than the focal length) the rays passing through the lens are diverging; they will never intersect on the far side of the lens. this distance is increasing

Converging Lens: Image Formation F F Is this image A.Real B.Virtual Recall that a virtual image means no light rays reach the image location. This configuration is what occurs when you use a magnifying glass.

Focal Length Remember we defined the focal length for a lens We also defined the sign of f. The focal length, f, is defined as positive for converging lenses and negative for diverging lenses. F F Focal length (f)

Lens Equation Quantities We also need to define some other distances. Object distance, d o Focal length, f Image distance, d i The object distance is positive for an object to the left of the lens. The image distance is positive for a (real) image on the right of the lens. These quantities are negative for the reverse situation. Be careful with this.

Lens Equation Quantities Focal length, f Object distance, d o Image distance, d i The image distance is negative for a (virtual) image on the left of the lens.

Lens Equation The lens equation expresses the quantitative relationship between the object distance (d o ), the image distance (d i ), and the focal length (f). The equation is stated as follows:

Practice Question A convex mirror has a focal length of cm. An object is placed 32.7 cm from the mirror's surface. Determine the image distance.

Practice Question A convex mirror has a focal length of cm. An object is placed 32.7 cm from the mirror's surface. Determine the image distance. Answer: d i = -8.1 cm Use the equation 1 / f = 1 / d o + 1 / d i where f = cm and d o = cm Substitute and solve for d i

Two equally true statements: The only thing we can hear is sound. The only thing we can see is light.

How do we see color? The color of an object is not actually within the object itself. Rather, the color is in the light that shines upon it and is ultimately reflected to our eyes.

How do we see color? When visible light strikes an object and a specific frequency becomes absorbed, that frequency of light will never make it to our eyes. Any visible light that strikes the object and becomes reflected to our eyes will contribute to the color appearance of that object. So the color is not in the object itself, but in the light that strikes the object and ultimately reaches our eye.

How do we see color? The only role that the object plays is that it might contain atoms capable of selectively absorbing one or more frequencies of the visible light that shine upon it. So (for example), if an object absorbs all of the frequencies of visible light except for the frequency associated with green light, then the object will appear green.

Check your understanding: White light shines on both papers. What color will each paper appear to be?

Transparent Objects Transparent materials allow one or more of the frequencies of visible light to be transmitted through them; whatever colors are not transmitted are typically absorbed by them. The appearance of a transparent object is dependent upon what colors of light are incident upon the object and what colors of light are transmitted through the object.

Check your understanding Two pieces of colored, transparent glass are shown below. What color are they?

Primary Colors When we speak of white light, we are referring to ROYGBIV - the presence of the entire spectrum of visible light. But combining all the frequencies in the visible light spectrum is not the only means of producing white light. White light can also be produced by combining only three distinct frequencies of light, provided that they are widely separated on the visible light spectrum. The three colors of light that produce white light when combined with the correct intensity are called primary colors of light. The most common set of primary colors is red, green, and blue.

Rods and Cones in the Retina: Remember, the cones are red, green, and blue.

Practice Question Which cones are sensitive to low-frequency visible light, which to medium-frequency visible light, and which to high-frequency visible light?

Interesting side note… The visible range and number of cone types differ between species. Mammals in general have color vision of a limited type, and are usually red-green color-blind, with only two types of cones. Humans, some primates, and some marsupials see an extended range of colors, but only by comparison with other mammals. Most non-mammalian vertebrate species distinguish different colors at least as well as humans, and many species of birds, fish, reptiles and amphibians have more than three cone types and probably superior color vision to humans.