Refraction & Lenses Chapter 18

Refraction of Light n Look at the surface of a swimming pool n Objects look distorted n Light bends as it goes from one medium into another\ n Why?

n When a medium causes a wave to slow down it is more optically dense

Entering more optically dense n Waves moving into a more optically dense medium will cause the wave speed to slow down and then bend toward the normal n Therefore, the angle of refraction is smaller than the angle of incidence

Entering less optically dense n Waves moving into a less optically dense medium will cause the wave speed to increase and then bend away from the normal n Therefore, the angle of refraction is larger than the angle of incidence

Snell’s Law n Dutch Scientist Willebrord Snell discovered that a ray of light bends in such a way that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant, index of refraction (n)

n i sin  i  n r sin  r n n i index of refraction for the incident medium  i angle of incidence n n r index of refraction for the refracting medium  r angle of refraction

Index of refraction n ratio of speed of light in a vacuum, c, to another medium, v n n=c/v n index of refraction in a vacuum is 1.00 n table on page 486

n If ray travels from a more optically dense into a less optically dense medium the angle of refraction is larger than the angle of incidence n Eventually the incidence angle is so great that all the light reflects back into the medium n No refraction takes place Total Internal Reflection

n The incident angle that causes the refracted ray to lie right along the boundary of the substance n Unique to each substance Critical Angle

water air critical ray Calculate the critical angle cc

n When light enters a thin glass rod light is internally reflected (fiber optics) n Telephone, computer and video signals n Explore the human body n Plants use internal reflection Total Internal Reflection

Effects of Refraction n Mirages n Summertime - the sun hits to road and causes the air above the road to heat up n The index of refraction for warm air is n The index of refraction for cool air is

n This small change in index of refraction causes the rays to bend n This bending makes the road look like there is a puddle on it

n Because light travels slightly slower in Earth’s atmosphere than in outer space the sun rays bend causing the sun to reach us before the sun is actually above the horizon n Same in the evening, the rays bend and reach us after the sun has actually set

Dispersion of Light n Light of all wavelengths travels at the same speed in a vacuum n Other media causes the speed to slow down n The wavelength also determines the speed & index of refraction

n In most materials red light travels fastest n It also has the smallest index of refraction n Violet is the slowest and has the largest index of refraction n Red is bent the least, violet the most

Dispersion n The separation of light into a spectrum by refraction n Diamond n Rainbow (water)

18.2 Convex & Concave Lenses n 1303 French physician wrote of using lenses to correct eyesight n 1610 Galileo used two lenses to make a telescope n He then discovered the moons of Jupiter n Now; microscopes, cameras, limitless uses

Type of Lenses n Lens-piece of transparent material used to focus light and form an image n Refractive index needs to be larger than air

Convex Lens n Thicker at the center than at the edges n Sometimes called a converging lens n Why? n What type of image will convex lenses produce? n Similar to concave mirrors

Concave Lens n Thinner in the middle than at the edges n Rays pass through the lens and spread out n Sometimes called a diverging lens n What type of images are formed? n Why? n Similar to convex mirrors

Lens Equations n Same as the mirror equations n Real images on the opposite side of the lens and the image n Real images d i is positive n Virtual images are always on the same side of the lens and d i is negative n Negative magnification means image is inverted and real

Real Images Formed by Convex Lens n No center of curvature, just F and 2F n F is the focal point and f is the focal length n Object needs to be placed beyond the focal point

Convex Lenses and Virtual Images n Object needs to be between the lens and the focal point n All rays diverge n Virtual image on the same side of the lens and larger in size

Concave Lens n Rays will always diverge n Always produce a virtual image n Same side of lens n Image will always be smaller

Ray Diagrams n Ray 1: Passes parallel to the principal axis to center of lens then bends to pass through the focal point n Ray 2: Passes through the focal point to the center of the lens and bends parallel to principal axis n Ray 3: Straight through the center of the lens at the principal axis

18.3 Applications of Lenses Lens in the Eye n Light travels through the cornea then the lens and then the image focuses on the retina n Retina works like the screen n The cells in the retina absorb this light and sends information about the image along the optic nerve to the brain

Focusing Images n Light is focused mostly by the air cornea boundary because this is the greatest difference in index of refractions n Lens does the fine focusing by accommodation (muscles around the lens contract, close up, or relax, far away) n changing the shape changes the focal length of the eye

Nearsightedness n Myopia, can’t focus on far away objects n Focal length too short so image forms in front of the retina n Use a diverging lens, concave lens, to spread the rays out so that the image distance increases

Farsightedness n Hyperopia, can’t focus on close up objects n The focal length of the eye is too long and the image forms behind the retina n Use a converging lens, convex lens, to produce a virtual images farther from the eye the image then becomes the object for the eye

n Also happens as a person gets older and the lens becomes more rigid, the muscles can’t change the shape of the lens