Chapter 15 Refraction

Chapter 15 Objectives Law of Refraction Snell’s Law Recognize the sign conventions for refracting surfaces Characterize images formed by thin lenses Recognize the sign conventions for thin lenses Utilize the lens maker’s equation Phenomena of the eye Total Internal Reflection Define Critical Angle

Refraction When a light ray encounters a boundary of a different density medium, part of the ray is reflected and the rest enters the medium. The portion that enters the new medium is bent slightly, or refracted.

Angle of Refraction The angle of refraction,  2, depends on –properties of the two media –angle of incidence Using those two qualities we can derive an index of refraction that is unique to each substance. –We use air as our reference material to have an index of refraction of n = 11 ’1’1 22

Snell’s Law Willebrord Snell (1591 –1626) is the man credited with the discovery of how light behaves when it changes medium. He saw a relationship between the angle of incidence and the speed of light traveling through that medium. –The density difference of the material created a change in the speed at which light travels through that medium. sin  2 sin  1 = v2v2 v1v1

Law of Refraction When light passes from one transparent medium to another, it is refracted because the speed of light is different in the two media. As light travels from one medium to another, its frequency does not change. That comes from the wave nature of light. –So if frequency stays the same, then wavelength and speed are the variables that can change.

Index of Refraction To establish a consistent system for how light behaves at boundary encounters, we establish an index of refraction. –That is, a relationship of how the speed of light changes from one substance to another. –And we use the speed of light in a vacuum as the baseline. So the smallest index of refraction is air, n = n == speed of light in a vacuum speed of light in the medium c v

Snell’s Law Revised With some mathematical manipulation, we can identify the angle of refraction by simply knowing the indices of the mediums in play. n 1 sin  1 n 2 sin  2 = angle of incidence angle of refraction

Images Formed by Refraction Lenses using the refraction property of light to perform their duties. –Whereas mirrors use the reflection property of light.

Sign Conventions for Spherical Lenses The sign conventions are the same as mirrors except when it comes to the image and the center of curvature. –p is positive if the object is in front of the lens. (real object) –p is negative if the object is behind the lens. (virtual object) –q is negative if the image is in front of the lens. (virtual image) –q is positive if the image is behind the lens. (real image) –R is negative if the center of curvature is in front of the lens. (concave lens) –R is positive if the center of curvature is behind the lens. (convex lens) –If M is positive, the image is upright. –If M is negative, the image is inverted.

Thin Lenses A typical thin lens consists of a piece of glass or plastic, ground so that each refracting surface is a segment of a sphere or plane. There are two types of thin lenses: –Converging lenses The initial surface of incidence is typically convex. This type of lens causes the rays to converge, or meet, at a single point after passing through. –Diverging lenses The initial surface of incidence is typically concave. This type of lens causes the rays to diverge, or separate, after passing through.

Focal Point of a Lens The focal point of a lens is found by the same method as a mirror. –That is the location that a set of parallel rays will intersect once they pass through the lens. There are two focal points for every thin lens because of the two refracting surfaces. –Light could enter from the left or the right! F

Focal Length of a Lens The focal length, ƒ, of a lens, and a mirror, is the image distance that corresponds to an infinite object distance. F ƒ ƒ = R 2

Magnification of a Lens The magnification formula and notation is the same for a lens as it was for a mirror. –Just remember the sign conventions are a little bit different based on the location of the image. M = image height object height = h’ h = q p – Negative sign shows the object is inverted. p is always positive, that way it acts as our point of reference. q is negative for a virtual image, and positive for a real image.

Thin Lens Equation The thin-lens equation looks and acts very similar to the mirror equation. –Except for the different sign conventions based on the location of the image. ƒ is positive for a converging lens ƒ is negative for a diverging lens 1 p + 1 q = 1 ƒ ƒ = R 2

Lens Maker’s Equation Because lenses have two refracting surfaces, we need to account for the radius of curvature for both surfaces. –Since the radius of curvature can be different for each surface, the thin lens equation turns into this more useful form: –Assuming that the lens is being used for light traveling through air. This will determine the overall focal length of any lens. 1 R1R1 + 1 R2R2 = 1 ƒ () (n – 1) Index of refraction of the lens material Radius of curvature of the front surface Radius of curvature of the rear surface

Ray Diagrams for Thin Lenses The first ray is drawn parallel to the principal axis and then refracted so it goes through the focal point of the incident surface. A second ray is drawn through the center of the lens and passes straight through to the other side. The last ray is drawn through the focal point of the rear surface of the lens and emerges from the rear surface parallel to the principal axis.

Internal Reflection Internal reflection can only occur when light attempts to travel from a medium with a high index of refraction to a medium with a lower index of refraction. At a particular angle of incidence called the critical angle,  c, the refracted light ray moves parallel to the reflecting boundary. –Refraction will occur when  1 <  c –Reflection will occur when  1 >  c This reflection will keep the light ray inside the original medium, thus internal reflection.

Calculating Critical Angle Knowing that the critical angle is found when the light ray is refracted parallel to the reflecting surface. –Plug 90 o into Snell’s Law as the angle of refraction, and you will see the following: n 1 sin  1 n 2 sin  2 = n 1 sin  c n 2 sin 90 o = n 1 sin  c n2n2 = sin  c n2n2 = n1n1

Fiber Optics Fiber optic cables use internal reflection to send a light pulse to a receiver. By knowing the critical angle of the fiber medium, the light source is transmitted at an angle larger than that so it will continue to internally reflect itself until it reaches its destination. –Fiber optic cables allow information to be transmitted faster because it uses light versus sound. Speed of light >>> speed of sound. –Fiber optic cables are better than using electrical pulses because the cables are less likely to build up heat. Heat creates resistance in electrical circuits. The first fiber optic semi-flexible gastroscope was patented by Basil Hirschowitz, C. Wilbur Peters, and Lawrence E. Curtiss, researchers at the University of Michigan, in 1956.

Dispersion Because Snell’s Law relates the angle of refraction to the wavelength of light, waves of differing lengths bend at different angles. In general, the index of refraction decreases as the wavelength increases. –So blue light ( =470 nm) will bend more than red light ( =650 nm)

Light Spectra Because of the effects of dispersion, the emerging light rays fan out to show the spectrum of light. –Every energy source has it unique spectrum. –Each energy source can be identified by its light spectrum much like people are identified by their fingerprints. A prism spectrometer is used to identify the “fingerprint” of any gas by emitting light at unique wavelengths.

Atmospheric Refraction