 Mirrors that are formed from a section of a sphere.  Convex: The reflection takes place on the outer surface of the spherical shape  Concave: The reflection surface is on the inner surface of the sphere.

 If objects are infinitely far away from a mirror (The sun, the stars, etc), the rays would be precisely parallel.  The law of reflection holds for each of the parallel rays and they will all reflect to be brought to a single point.

 Ray 1: drawn parallel to the principle axis, and then passes through the focal point after reflection.

 Ray 2: drawn through F; therefore must reflect parallel to the principle axis.

 Ray 3: Perpendicular to the mirror, passes through the radius of curvature.

 Ray 1 goes from object parallel to the axis and reflects through the focal point.  Ray 2 goes from object through focal point and reflects parallel to the axis.  Ray 3 goes from object, perpendicular to the mirror, reflects back on itself through the center of curvature.

 Virtual Image: If a film or paper were placed in the location of the image, rays would not actually pass through this location.  Real Image: light does pass through the location of the image. If a film were placed at the image position, light would be put onto the film.

 We could always use ray diagrams, but accuracy is difficult.  Mirror equation S represents distance of image and object. f represents the focal length.

 Magnification is the image height divided by the object height.  Sign conventions  Positive image height means upright, negative is inverted relative to the object.  Positive distance is in front of the mirror, and negative is behind the mirror.

 A 1.50 cm high diamond ring is placed 20 cm from a concave mirror whose focal length is 15 cm. Determine the position and size of the image.

 The speed of light in a vacuum is 3.0x10 8 m/s  In other mediums, the speed of light is less.  We call the ratio of the speed of light in a vacuum to the speed of light in another medium the index of refraction

 Can a material’s index of refraction ever be less than 1?  Some indices of refraction that are useful: Air – Water – 1.33 Crown glass – 1.52 Lucite (Plexiglass) – 1.51 Diamond – 2.42

 When light hits the boundary of two mediums, some of the light is reflected and some passes into the new medium.  Since the ray of light will be traveling at a different speed, its path is bent.  This is called refraction.  Bending Light - Index of Refraction, Light, Snell's Law - PhET Bending Light - Index of Refraction, Light, Snell's Law - PhET

 As light passes from a medium with a low index of refraction to one with a higher index, the light ray will be refracted towards the normal.

 As light travels from a medium with a higher index of refraction to one with a smaller index, the light is refracted away from the normal.

 Remember, angle of incidence and now angle of refraction, are both measured from the normal

 As light passes from one material to another where the index of refraction is less (water into air for example), the light bends away from the normal.  At a particular incident angle, the angle of refraction will be 90 degrees.  This is called the critical angle.

 The incident light is at such an angle that all of the light is reflected.  This will only occur if n1 > n2  Many technological usages of total internal reflection:  Binoculars  Fiber optics  endoscopes

 A lens is made up of two faces that are usually portions of a sphere.  The two faces can be either concave or convex.  We only use thin lenses in this class which means that the diameter of the lens is small compared to the radii of curvature of the two lens surfaces.

 Converging lens: a lens that is thicker in the center than at the edges makes parallel rays converge to a point.  Diverging lens: a lens that is thinner in the center than at the edges makes parallel rays diverge.  The focal point is defined as the point from which refracted rays seem to have emerged from as a single point.

 Ray 1: parallel to the axis and then refracted through the focal point on the opposite side.

 Ray 2: Passes through the F’ on the same side of the lens as the object and then goes parallel to the axis beyond the lens.

 Ray 3: directed towards the very center of the lens, and emerges the same angle as it entered.

 Ray 1: leaves the top of the object going parallel to the axis and then refracts through the focal point.  Ray 2: passes through F’ and leaves the lens parallel to the axis.  Ray 3: goes straight from the object through the center of the lens and back out the same angle.

 Notice, that in the case of a lens, the light of the image, on the opposite side of the lens, is able to be detected by film.  Opposite than a mirror, a real image is on the opposite side of the lens.  A virtual image is on the same side of the lens.

 Luckily it is the same as the mirror equations

 The focal length is positive for converging lenses and negative for diverging lenses.  The object distance is positive if it is on the side of the lens from which the light is coming (this is usually the case, although when lenses are used in combination, it might not be so); otherwise, it is negative

 The image distance is positive if it is on the opposite side of the lens from where the light is coming; if it is on the same side, then it is negative. If the image distance is positive, then the image is real.  The height of the image is positive it if it is upright.

 What is the position and the size of the image of a large 7.6 cm high flower placed 1.0 m from a +50 mm focal length camera lens?