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.

i i > r r Example: light slows down when it passes from air 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 n i air i > r water r

i r i < r n Example: light speeds up when passing from 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 i n r glass 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 any 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.

n1 sin q1 = n2 sin q2 This relationship is known as Snell’s Law. q1 n1 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 whenever light passes from a vacuum into the substance. In general, for light passing from medium 1 into medium 2, n1 sin q1 = n2 sin q2 This relationship is known as Snell’s Law. q1 n1 n2 q2

sin qc = 1/n Total Internal Reflection may occur when light enters a new medium and speeds up (bends away from the normal). Investigate 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 qc = 1/n

Click here, here, and here to view simulations of Snell’s Law. View an analytical derivation of the geometrical relationship here. Investigate total internal reflection 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 convex plano-convex concavo-convex These lenses converge light to a real focus.

Diverging Lenses - thicker at edge than in middle double concave plano-concave convexo-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.

Ray Diagrams 1/f = 1/do + 1/di di/do = si/so. 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/do + 1/di and di/do = si/so.

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

The PhET simulation linked here shows image formation in a converging lens. Learn more about image characteristics here. 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 image characteristics depend on the object’s position with respect to one and two focal lengths (1f and 2f) away from the lens. 2f f

object is beyond two focal lengths: image is real, inverted, and reduced 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

The simulation linked to the optics applets here shows image formation in all types of lenses and curved mirrors. Learn more about image characteristics here. 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

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