Where should the fisherman aim? The fish is not moving.

Where should the fisherman aim? The fish is not moving.

When a wave hits a boundary it can Reflect Refract Reflect and Refract Be Absorbed

Refraction The change in speed and direction of a wave Due to change in medium Must cross boundary at an angle other than 90 o, otherwise no change in direction I R (unlike reflection) Amount of bending is determined by Optical Density of the media

What do you think? Will a light wave travel faster or slower as it enters more dense media? Slower If the speed changes, will the frequency change? No, just the wavelength If the speed travels slower, what will happen to the wavelength? It will decrease What is the maximum speed? The speed of light

For refraction of light: the wave speed is always greatest in the medium least dense the wavelength is always greatest in the medium least dense the frequency of a wave does when crossing a boundary does not

For refraction of light: When light passes from a more optically dense medium into a less optically dense medium, it will bend the normal. Away When light passes from a less optically dense medium into a more optically dense medium, it will bend the normal. Towards

The normal line is drawn perpendicular to the boundary between the media θ i θ r = angle of incidence = angle of refraction

Diagrams of Refraction Less dense Incident Ray Normal θ i Boundary θ r Refracted Ray More dense

Diagrams of Refraction More dense Incident Ray Normal θ i Boundary θ r Refracted Ray Less dense

Memory trick AWAY FAST GAS TOWARDS SLOW SOLID

Review: When light passes from a more optically dense medium into a less optically dense medium, it will bend the normal. Away When light passes from a less optically dense medium into a more optically dense medium, it will bend the normal. Towards

Demo: Cornstarch Oil stirring rod Penny Stirring rod and letters

Incident Ray What do you think will happen to the light ray on the other side?

Light rays that strike the parallel sided glass figure perpendicular to the side will pass straight through the piece of glass without bending. Incident Ray Emergent Ray

What do you think will happen to the light ray on the other side? Incident Ray

Refraction Diagram WS

Aim in front He must aim at a position on the water below where the fish appears to be. Since light refracts away from the normal (water to air) as Arthur sights at the fish, the refracted ray when extended backwards passes over the head of where the fish actually is.

Mirages 18

Rainbows Interesting tidbit: Sun is behind you for you to see a rainbow 19

Rainbows are due to refraction and reflection in water droplets 20

How do we quantify optical density? We know light travels at 3 x 10 8 m/s in a vacuum We know as optically density of medium increases, light speed decreases

Optical Density Described by Index of Refraction n stands for the index A measure of the ratio of light speed traveling in a vacuum and light speed traveling in another medium

Index of Refraction n c v substance Where n = index of refraction c = speed of light in a vacuum v = velocity of light in medium

Index of Refraction What is n in a vacuum? n = exactly 1 in a perfect vacuum How do you think the speed of light changes in air? Very little. Speed in air = 2.9991 x 10 8 m/s. What would be n air n = 1.0003 in air not significant, so use n=1 for air n > 1 for all materials As density increases, what will happen to the index of refraction? It increases

Ex 1 The speed of light in a type of plastic is 2.00 x 10 8 m/s. What is the index of refraction for the plastic? n = c/v n = 3.00 x 10 8 m/s 2.00 x 10 8 m/s n = 1.5 Did light travel faster or slower upon entering the plastic? Slower How did the frequency change? It doesn t How would the wavelength change? It would decrease

Ex 2 What is the speed of light as it travels through water? n water = 1.33 n = c/v v sub = c/n v sub = 3.00 x 10 8 m/s 1.33 v sub = 2.26x 10 8 m/s

NO UNIT FOR Index of refraction. It is a ratio

Mirages 28

Rainbows Interesting tidbit: Sun is behind you for you to see a rainbow 29

Rainbows are due to refraction and reflection in water droplets 30

Google Image Result for http://www.rebeccapaton.net/rainbows/rn bwbmp.gif

Refraction and Lenses

The most common application of refraction in science and technology is lenses. The kind of lenses we typically think of are made of glass or plastic. The basic rules of refraction still apply but due to the curved surface of the lenses, they create images.

real image inverted image on opposite side of lens from object where light rays actually converge ( cross ) can project on screen (Your retina is a screen ) virtual image upright image on the same side of lens as object where light rays appear to cross not projectable

REAL IMAGE FORMATION BY LENSES

VIRTUAL IMAGE FORMATION BY LENSES

Two main types of lenses Converging (convex) Diverging (concave) focal length (f) of a lens depends on: shape index of refraction

Converging Lenses = Convex Lenses thick in the center and thin at the edges focus light rays farsightedness (hyperopia) form virtual images (upright & enlarged) when object inside f aka magnifying Lenses Forms real images when object beyond f Object is here. This is the Front. f Eye here. Behind lens

Diverging Lenses = Concave Lenses thin in the center and thick at the edges spread out light rays for nearsightedness (myopia) virtual images only (where refracted rays appear to cross always upright and reduced aka reducing lenses Object is here. This is the Front. f Eye here. Behind lens

CONVEX LENSES Where is the object when the image is the same size? Where is the object when there is no image?

The eye contains a convex lens. This lens focuses images on the back wall of the eye known as the retina.

VISION PROBLEMS: MYOPIA is when image is formed in front of retina and is also known as nearsightedness and is corrected with a concave lens

Someone who is nearsighted can see near objects more clearly than far objects. The retina is too far from the lens and the eye muscles are unable to make the lens thin enough to compensate for this. Diverging glass lenses are used to extend the effective focal length of the eye lens.

VISION PROBLEMS: HYPEROPIA is when image is formed behind the retina and is also known as farsightedness and is corrected with a convex lens

Someone who is farsighted can see far objects more clearly than near objects. The retina is now too close to the lens. The lens would have to be considerable thickened to make up for this. A converging glass lens is used to shorten the effective focal length of the eye lens. Today s corrective lenses are carefully ground to help the individual eye but cruder lenses for many purposes were made for 300 years before the refractive behavior of light was fully understood.

VISION PROBLEMS: ASTIGMATISM is when the eye is shaped like a football rather than the normal eye that has a round shape similar to basketball. It causes certain amounts of distortion or pitched images because of the uneven bending of light rays entering the eye.

Lens Equation (1/f) = (1/d o ) + (1/d i ) f = focal length d o = object distance d i = image distance

Lens Magnification Equation M = -(d i / d o ) = (h i / h o ) M = magnification d i = image distance d o = object distance h i = image height h o = object height

f d i d o h i h o M Lens Sign Conventions + for Converging Lenses - for Diverging Lenses + for images on opposite side of lens from object (real) - for images on same side of lens as object (virtual) + always + if upright image - if inverted image + always + if virtual - if real image Magnitude of magnification <1 if smaller =1 if same size

Ex. 7 Camera lenses are described in terms of their focal length. A 50 mm lens has a focal length of 50 mm. Do cameras use converging or diverging lenses? What does d i represent? a. Where is the image (from the lens) of the above camera when it is focused on an object 3.0 meters away? b. What is the magnification of the image? c. If the object is 1.5 m tall, what is the height of the image? (Students need to add this to their notesheet)

Ex. 7 Camera lenses are described in terms of their focal length. A 50 mm lens has a focal length of 50 mm. Do cameras use converging or diverging lenses? Converging Convex What does d i represent? The location of the image on the film a. Where is the image (from the lens) of the above camera when it is focused on an object 3.0 meters away? f = 50 mm do = 3m = 3000mm 1/f = 1/d o + 1/d i 1/d i = 1/f - 1/d o 1/d i = 1/50mm - 1/3000mm 1/d i = 0.019667mm d i = 50.85mm

Ex. 7 Camera lenses are described in terms of their focal length. A 50 mm lens has a focal length of 50 mm. f = 50 mm do = 3m = 3000mm di = 50.85mm b. What is the magnification of the image? M = -d i /d o M = -50.85mm/3000mm M = -0.017 Negative means it is real; 0.017 means it is reduced

Ex. 7 Camera lenses are described in terms of their focal length. A 50 mm lens has a focal length of 50 mm. f = 50 mm do = 3m = 3000mm di = 50.85mm M = -0.017 c. If the object is 1.5 m tall, what is the height of the image? (Students need to add this to their notesheet) M = h i /h o h i = Md o h i = (-0.017) (1.5m) h i = -0.026m Negative means it is real

Rules for Locating Refracted Images 1. Start at top of object. Light rays that travel through the center of the lens (where the principle axis intersects the midline) are not refracted and continues along the same path. 2. Start at top of object. Light rays that travel parallel to the principle axis, strike the lens, and are refracted through the focal point (f).

Images formed by Convex lenses

Locating images in convex lenses

Convex Lenses with the Object located beyond 2f

Convex Lens Object located beyond C C C f f Light rays that travel through the center of the lens are not refracted and continue along the same path.

Convex Lens Object located beyond 2f 2f 2f f f Light rays that travel parallel to the principle axis, strike the lens, and are refracted through the focal point (f).

Convex Lens Object located beyond 2f 2f Image: Real Inverted Smaller 2f f f The image is located where the refracted light rays intersect

Convex Lenses with the Object located at 2f

Convex Lens Object located at 2f 2f 2f f f Light rays that travel through the center of the lens are not refracted and continue along the same path.

Convex Lens Object located at 2f 2f 2f f f Light rays that travel parallel to the principle axis, strike the lens, and are refracted through the focal point (f).

Convex Lens Object located at 2f 2f Image: 2f f f Real Inverted Same Size The image is located where the refracted light rays intersect

Convex Lenses with the Object located between f and 2f

Convex Lens Object located between f and 2f 2f 2f f f Light rays that travel through the center of the lens are not refracted and continue along the same path.

Convex Lens Object located between f and 2f 2f 2f f f Light rays that travel parallel to the principle axis, strike the lens, and are refracted through the focal point (f).

Convex Lens Object located between f and 2f 2f Image: 2f f f Real Inverted Larger Beyond 2f The image is located where the refracted light rays intersect

Convex Lenses with the Object located at f

Convex Lens Object located at f 2f 2f f f Light rays that travel through the center of the lens are not refracted and continue along the same path.

Convex Lens Object located at f 2f 2f f f Light rays that travel parallel to the principle axis, strike the lens, and are refracted through the focal point (f).

All refracted light rays are parallel and do not cross Convex Lens Object located at f 2f 2f No image is formed. f f

Convex Lenses with the Object located between f and the lens

Convex Lens Object located between f and the lens 2f 2f f f Light rays that travel through the center of the lens are not refracted and continue along the same path.

Convex Lens Object located between f and the lens 2f 2f f f Light rays that travel parallel to the principle axis, strike the lens, and are refracted through the focal point (f).

Convex Lens Object located between f and the lens 2f 2f f f These to refracted rays do not cross to the right of the lens so we have to project them back behind the lens.

Convex Lens Image: 2f Virtual Upright Larger Further away f f Object located between f and the lens 2f The image is located at the point which the refracted rays APPEAR to have crossed behind the lens

Images formed by concave lenses

Locating images in concave lenses

Concave Lenses with the Object located anywhere

Concave Lens Object located anywhere 2f f f 2f Light rays that travel through the center of the lens are not refracted and continue along the same path.

Concave Lens Object located anywhere 2f f f 2f Light rays that travel parallel to the principle axis, strike the lens, and are refracted through the focal point (f).

Concave Lens Object located anywhere Image: Virtual 2f f f 2f Upright Smaller Between f and the lens The image is located where the refracted light rays appear to have intersected