the change of direction of a ray of light as it passes obliquely from one medium into another of different transmission speed Optical Density of a medium refers to the speed of light in that medium. It does not necessarily correspond to the Mass density of that material.

When light travels from a less dense to more dense medium (light slows down), the ray is refracted toward the normal. Example: light slows down when it passes from air into water air water n i r i>r

When light travels from a more dense medium to a less dense medium (light speeds up), the ray is refracted away from the normal. Example: light speeds up when passing from glass into air air glass n i r i < r

An object’s ability to decrease the speed of light, and therefore cause refraction, is given by its index of refraction. By definition: the index of refraction of a transparent substance is equal to the speed of light in a vacuum divided by the speed of light in that substance. n = c / v n = (3 x 108 m/s) / v

The table to the left shows values of the index of refraction for some common substances. The larger the index of refraction, the slower that light travels through the substance.

angles of incidence and refraction The angles of incidence and refraction are related in such a way that n = (sin i)/(sin r), where i = angle of incidence and r = angle of refraction vacuum whenever light passes from a vacuum into the substance. In general, for light passing from medium 1 into medium 2, n1 sin 1 = n2 sin 2 This relationship is known as Snell’s Law. Snell’s Law n1n1 n2n2 11 22

Total Internal Reflection may occur when light enters a new medium and speeds up (bends away from the normal). Investigate here. here The maximum angle of incidence in which light may enter air from another substance and not undergo total internal refraction is known as the critical angle, and is related to the index of refraction of the substance by: sin c = 1/n

Click here, here, Click here, here,here and here to view and here to viewhere simulations of Snell’s simulations of Snell’s Law. Law. View an analytical derivation of the geometrical relationship here. here

LENS any transparent object having two nonparallel curved surfaces or one plane surface and one curved surface Converging Lenses - thicker in middle than in the edge double convexplano-convexconcavo-convex These lenses converge light to a real focus.

double concaveplano-concave These lenses diverge light from a virtual focus. The focal length of a lens is generally NOT half-way between the center of curvature and the vertex of the lens, but it depends on the lens material’s index of refraction and on the shape of the lens. Diverging Lenses - thicker at edge than in middle convexo-concave

Ray Diagrams Converging and Diverging Lenses 1. Rays passing through the optical center pass straight through without refraction. 2. Incident rays parallel to the principal axis refract through the focus or diverge away from the focus. 3. Rays passing through or toward the focus refract parallel to the principal axis. Just like mirrors, 1/f = 1/d o + 1/d i and d i /d o = s i /s o.

Click here, here, and here to view here simulations showing image formation in converging and diverging lenses using these three important rays.

Images formed by converging lenses may be: 1. real, virtual, or non-existent 2. upright or inverted 3. reduced, enlarged, or same size 4. in front or behind the lens The PhET simulation linked here here shows image formation in a converging lens. Learn more about image characteristics here. here

The image characteristics depend on the object’s position with respect to one and two focal lengths (1f and 2f) away from the lens. 2ff

object is exactly twice the focal length: image is real, inverted, and the same size object between one and two focal lengths: image is real, inverted, and enlarged object is on the focus: no image; rays reflect parallel object is inside the focus: image is virtual, upright, and enlarged object is beyond two focal lengths: image is real, inverted, and reduced

Images formed by diverging lenses are always: 1. virtual 2. upright 3. reduced 4. located in front of the lens between the focus and the lens focus and the lens The simulation linked to the optics applets herehere shows image formation in all here types of lenses and curved mirrors. Learn more about image characteristics here. here

General Image Trends real images are always inverted real images are always inverted virtual images are always upright virtual images are always upright real images are always behind the lens real images are always behind the lens virtual images are always in front virtual images are always in front of the lens negative image distance means negative image distance means virtual image positive image distance means real image positive image distance means real image real images may be projected onto a screen; virtual images may not real images may be projected onto a screen; virtual images may not