Chapter 32Light: Reflection and Refraction

30-6 LC Oscillations with Resistance (LRC Circuit) Any real (nonsuperconducting) circuit will have resistance.

30-6 LC Oscillations with Resistance (LRC Circuit ) Now the voltage drops around the circuit give

30-6 LC Oscillations with Resistance (LRC Circuit) This figure shows the three cases of underdamping A ( R 2 4L/C), and critical damping B ( R 2 = 4L/C).

30-6 LC Oscillations with Resistance (LRC Circuit) The angular frequency for underdamped oscillations is given by The charge in the circuit as a function of time is..

Analyzing the LRC series AC circuit is complicated, as the voltages are not in phase – this means we cannot simply add them. Furthermore, the reactances depend on the frequency LRC Series AC Circuit

We calculate the voltage (and current) using what are called phasors – these are vectors representing the individual voltages. Here, at t = 0, the current and voltage are both at a maximum. As time goes on, the phasors will rotate counterclockwise LRC Series AC Circuit

The voltages across each device are given by the x-component of each, and the current by its x- component. The current is the same throughout the circuit LRC Series AC Circuit The sum of all voltages is the instantaneous voltage

We find from the ratio of voltage to current that the effective resistance, called the impedance, of the circuit is given by 30-8 LRC Series AC Circuit X L : reactance of the inductor=2πfL X c : reactance of the capacitor=1/2πfC

30-8 LRC Series AC Circuit The phase angle between the voltage and the current is given by The factor cos φ is called the power factor of the circuit. or

31-3 Maxwell’s Equations This set of equations describe electric and magnetic fields, and is called Maxwell’s equations. In the absence of dielectric or magnetic materials, they are: A electric field induce a magnetic field A magnetic field induce a electric field

Since a changing electric field produces a magnetic field, and a changing magnetic field produces an electric field, once sinusoidal fields are created they can propagate on their own. These propagating fields are called electromagnetic waves (EM) Production of Electromagnetic Waves

Induced Electric Fields Electric & Magnetic fields induce each other Changing E  changing B Changing B induces emf  changing E  create electromagnet ic waves

Electromagnetic Waves Waves made of oscillating electric and magnetic fields Produced by ACCELERATING charges E B

Electromagnetic Waves Charge accelerates this creates a changing B-field By Faraday’s Law of induction this creates a changing E-field E B

31-5 Electromagnetic Waves, and Their Speed, Derived from Maxwell’s Equations B and E are related by the following equation Here, v is the velocity of the wave.. The magnitude of this speed is around 3.0 x 10 8 m/s – precisely equal to the measured speed of light. Maxwell’s argue that light in EM wave after this calculation

Speed of EM Waves -- vacuum EM waves do not require a medium to propagate Permittivity of free space   = 8.85 x C 2 /N  m 2 Permeability of free space:   = 4  x T  m/A Galaxy 2 million ly away

The frequency of an electromagnetic wave is related to its wavelength and to the speed of light: 31-6 Light as an Electromagnetic Wave and the Electromagnetic Spectrum

Speed of Light in matter Generally light slows down when it encounters a medium other than vacuum. n is the index of refraction of the medium n≥1 c n v Frequency is unchanged  

Electromagnetic waves can have any wavelength; we have given different names to different parts of the wavelength spectrum Light as an Electromagnetic Wave and the Electromagnetic Spectrum

Light very often travels in straight lines. We represent light using rays, which are straight lines emanating from an object. This is an idealization, but is very useful for geometric optics The Ray Model of Light

Law of reflection: the angle of reflection (that the ray makes with the normal to a surface) equals the angle of incidence Reflection; Image Formation by a Plane Mirror

When light reflects from a rough surface, the law of reflection still holds, but the angle of incidence varies. This is called diffuse reflection Reflection; Image Formation by a Plane Mirror

With diffuse reflection, your eye sees reflected light at all angles. With specular reflection (from a mirror), your eye must be in the correct position Reflection; Image Formation by a Plane Mirror

What you see when you look into a plane (flat) mirror is an image, which appears to be behind the mirror Reflection; Image Formation by a Plane Mirror

This is called a virtual image, as the light does not go through it. The distance of the image from the mirror d i is equal to the distance of the object from the mirror d Reflection; Image Formation by a Plane Mirror

Example 32-1: Reflection from flat mirrors. Two flat mirrors are perpendicular to each other. An incoming beam of light makes an angle of 15° with the first mirror as shown. What angle will the outgoing beam make with the second mirror?

Problem 4 4.(II) A person whose eyes are 1.64 m above the floor stands 2.30 m in front of a vertical plane mirror whose bottom edge is 38 cm above the floor, Fig. 32–46. What is the horizontal distance x to the base of the wall supporting the mirror of the nearest point on the floor that can be seen reflected in the mirror?

Spherical mirrors are shaped like sections of a sphere, and may be reflective on either the inside (concave) or outside (convex) Formation of Images by Spherical Mirrors

Spherical Mirrors Convex Like you are in a cave Concave

Rays coming from a faraway object are effectively parallel Formation of Images by Spherical Mirrors

Parallel rays striking a spherical mirror do not all converge at exactly the same place if the curvature of the mirror is large; this is called spherical aberration Formation of Images by Spherical Mirrors

If the curvature is small, the focus is much more precise; the focal point is where the rays converge Formation of Images by Spherical Mirrors :Focal point :Focal length Center of curvature:

Spherical Mirrors: Concave 1.Parallel ray goes through f 2.Ray through center reflects back 3.Ray through f comes out parallel C f object image ujava/index.php?topic=48 Upright or upside down Real or virtual Bigger or smaller Image:

Spherical Mirrors: Convex Radius of Curvature Principle axis Focal point f=R/2 Center of Curvature 1.Parallel ray goes through f 2.Ray through center reflects back 3.Ray through f comes out parallel R C f object image Image: Upright or upside down Real or virtual Bigger or smaller

The intersection of the three rays gives the position of the image of a point on the object. To get a full image, we can do the same with other points (two points suffice for many purposes). Because the light passes through the image itself, this is called “Real image” Formation of Images by Spherical Mirrors

Geometrically, we can derive an equation that relates the object distance, image distance, and focal length of the mirror: 32-3 Formation of Images by Spherical Mirrors

Using geometry, we find that the focal length is half the radius of curvature: The More curved is the mirror, the worse is the approximation and the more blurred is the image. Spherical aberration can be avoided by using a parabolic reflector; these are more difficult and expensive to make, and so they are used only when necessary, such as in research telescopes Formation of Images by Spherical Mirrors

Example 32-7: Convex rearview mirror. An external rearview car mirror is convex with a radius of curvature of 16.0 m. Determine the location of the image and its magnification for an object 10.0 m from the mirror.