Chapter 22 Reflection and Refraction of Light Herriman High AP Physics 2

Nature of Light  Light has a dual nature. This means that it exhibits properties of both waves and particles. The current definition of light is a photon of energy carried by or upon a wave front.  A Photon is a discrete packet of energy. The visible spectrum is the range of wavelengths of electromagnetic radiation which stimulate the human retina (4 x m < λ < 7.5 x m).  White light is a combination of all colors of the visible spectrum, while black is the absence of all colors. Herriman High AP Physics 2

Colors of Light  White light can be separated into its component colors by diffraction which is the bending of light. Colors of light which have the longest wavelength have the lowest frequency and those with the shortest wavelength have the highest frequency.  The visible spectrum of light, has the following component colors listed from lowest frequency (longest wavelength) to highest frequency (shortest wavelength) Herriman High AP Physics 2 REDRED ORANGEORANGE YELLOWYELLOW GREENGREEN BLUE BLUE INDIGOINDIGO VIOLETVIOLET

Quantum Theory of Light  Quantum Theory - an electron in the electron can only absorb energy if that energy is enough to move it to the next level in the cloud.  This moves the electron from its normal or ground state to a higher energy or excited state. In order to lose this extra, set amount of energy, the electron gives off light.  Max Planck found that the color or frequency of light given off corresponded to the amount of energy given off according to the equation: E = hf  Where h is a constant = x Js and f = the frequency of light given off. Hence energy is in joules. Herriman High AP Physics 2

Reflection  When a wave reaches a boundary between two media and is turned back – this is reflection Total reflection –boundary with a more rigid medium Partial reflection – less rigid medium. This can be analyzed using the ray model of light, i.e. representing a light wave with a ray. Herriman High AP Physics 2

Law of Reflection  The law of reflection states that the angle of incidence = angle of reflection Incident ray Reflected ray Angle of incidence Angle of reflection Herriman High AP Physics 2

Refraction  Refraction is the bending of light at a boundary.  If the speed in the new media is less than the speed in the old, the wave bends toward the normal  If the speed in the new media is more than the speed in the old, the wave bends away from the normal. Sidewalk Grass Herriman High AP Physics 2

Snell’s Law and the Index of Refraction  How much light bends at a boundary is given by Snell’s Law or the Index of refraction: Another way that this law is written is: n 0 sin i = n sin r Where n 0 is the index for the material you are moving out of and n is the index for the material you are going into. Herriman High AP Physics 2

Sample Problem  What is the speed of light in crown glass if its index of refraction is 1.52?  What is the angle of refraction for a wave in crown glass if its angle of incidence is 30°. Assume that it is coming from air into a cube of the glass. Herriman High AP Physics 2

Solution n 0 sin i = n sin r 1 sin 30° = 1.52 sin r 1 sin 30°/1.52 = sin r r = 19.73° Herriman High AP Physics 2

Dispersion and Prisms  The angle of refraction made when light enters a material depends upon the wavelength of the light.  White light enters a prism and is diffracted – separating into its component colors called the spectra.  This is also how and why a rainbow forms. Herriman High AP Physics 2

Total Internal Reflection Herriman High AP Physics 2

Chapter 23 Mirrors and Lenses Herriman High AP Physics 2

Mirrors  Plane mirrors are flat mirrors which form a virtual image. A virtual image is one which forms on the opposite side of the mirror. Images are the same size as the object and the same vertical orientation. Herriman High AP Physics 2

Image in a Plane Mirror  Seeing yourself in a plane mirror requires that the mirror be at least ½ the height of the object  You see your head looking straight across  You see your feet looking down, since the ray passes through the mirror at ½ the distance between you and the image so the mirror, by similar triangles must be ½ your height. Herriman High AP Physics 2

Plane Mirrors: Things to Remember  Images are virtual – i.e behind the mirror  Images are the same distance from the mirror as the object  Images are upright  Images are the same size as the object.  Images are inverted right to left. Herriman High AP Physics 2

Curved Mirrors  Vocabulary Principal Axis – line perpendicular to mirror passing through the center of curvature and the focal point. Center of Curvature – the geometric center of the sphere from which the mirror was formed Focal length – ½ the center of curvature Image Distance – distance from the mirror to where the image is formed Object Distance – distance from mirror to object. Herriman High AP Physics 2

Curved Mirrors  Any light ray which approaches the mirror parallel to the principal axis will be reflected through the focal point.  Any light ray which passes through the focal point will be reflected parallel to the principal axis. Herriman High AP Physics 2

Curved Mirrors: Concave  Concave Mirror Curves inward Close objects Form a virtual image which is larger than the object Objects further away form real images which are cast on a screen Herriman High AP Physics 2

Curved Mirrors: Convex  Convex Mirror Curves outward Close objects form a virtual image which is smaller than the object These mirrors are used to give a wide field of view Herriman High AP Physics 2

Image Object Relationships  f = focal length  d i (q)= distance to image  d 0 (p) = distance to object  h i (h’)= height of image  h 0 (h)= height of object  For convex mirrors, f is negative Herriman High AP Physics 2

Sample Problem  If an object which is 3 cm in diameter is placed 10 cm from a convex mirror with a focal length of 5 cm, where will the image appear, how large will it be, and will it be upright or inverted? Herriman High AP Physics 2

Solution The image appears on the opposite side of the mirror and is 1/3 as large and is upright. Herriman High AP Physics 2

Converging and Diverging Lenses  Converging lenses are convex, or curve outward.  Diverging lenses are concave, or curve inward. Herriman High AP Physics 2

Sign Conventions for Lenses  Lenses use the same equations as mirrors  The following rules apply to lenses: The focal length is positive for a converging lens and negative for a diverging lens. Object distance is positive Image distance is positive if it is on the opposite side of the lens from the object and negative if it is on the same side as the object. The height of the object is always taken to be positive. The image height is positive if it is upright and negative if it is inverted. Herriman High AP Physics 2

Sample Problem  If an object which is 2 cm in diameter is placed 12 cm from a convex lens with a focal length of 5 cm, where will the image appear, how large will it be, and will it be upright or inverted? Herriman High AP Physics 2

Solution The image appears on the opposite side of the lens and is 0.7 x as large and is inverted. Herriman High AP Physics 2

The Eye  The lens of a human eye focuses an image on the retina at the rear of the eye.  If the lens forms an image in front of the retina, then a person is said to be nearsighted  If the lens form an image at the rear of the retina (behind it) then the person is said to be farsighted. Herriman High AP Physics 2

Corrective Lenses  Since a nearsighted person’s eye forms the image too soon, the lens of their eye has too much convergence, hence a diverging lens, (concave) is used to separate the rays of light coming from the object so that the image will converge on the retina.  Since a Farsighted person’s eye forms the image after the retina, a converging lens, (convex) is used to help the rays of light converge sooner, forming the image on the retina. Herriman High AP Physics 2