1. University Physics Midterm Exam Overview

2. 16. THE NATURE OF LIGHT Speed of light c = 3x10 8 m/s (in the vacuum) v = c/n (in the media) Formulas c = f =  f = 1/T  (How to memorize? Think about v=d/t.) 

3. Refraction and Reflection The incident ray, the reflected ray, the refracted ray, and the normal all lie on the same plane What is the normal? How to find angle of incidence and angle of refraction?

4. Snell’s Law n 1 sin θ 1 = n 2 sin θ 2 θ 1 is the angle of incidence θ 2 is the angle of refraction

5. As light travels from one medium to another its frequency (f) does not change But the wave speed (v=c/n) and the wavelength ( med = /n) do change

6. 17. THIN LENSES Magnification Thin Lens Equation QuantityPositive “+”Negative “-” s - Object DistanceFront*Back* s’ - Image Distance Back* Real Front* Virtual f - Focal Length (f)Converging “()”Diverging “)(” h – Image HeightUprightInverted

7. Combination of Thin Lenses

8. Spherical Mirrors Focal length is determined by the radius of the mirror

9. Corrective Lenses Nearsighted correction – bring infinity to the far point image distance = - far point (upright virtual image) object distance = ∞ Farsighted correction – bring the close object (accepted 25 cm) to the near point of farsighted image distance = - near point (upright virtual image) object distance = 25 cm Power of the Lens P=1/f (in diopters or m -1 )

10. 18. Wave Motion A wave is the motion of a disturbance Mechanical waves require Some source of disturbance A medium that can be disturbed Some physical connection between or mechanism though which adjacent portions of the medium influence each other All waves carry energy and momentum

11. Types of Waves – Traveling Waves Flip one end of a long rope that is under tension and fixed at one end The pulse travels to the right with a definite speed A disturbance of this type is called a traveling wave

12. Types of Waves – Transverse In a transverse wave, each element that is disturbed moves in a direction perpendicular to the wave motion

13. Types of Waves – Longitudinal In a longitudinal wave, the elements of the medium undergo displacements parallel to the motion of the wave A longitudinal wave is also called a compression wave

14. Speed of a Wave v = λ ƒ Is derived from the basic speed equation of distance/time This is a general equation that can be applied to many types of waves

15. Speed of a Wave on a String The speed on a wave stretched under some tension, F  is called the linear density The speed depends only upon the properties of the medium through which the disturbance travels

16. Waveform – A Picture of a Wave The brown curve is a “snapshot” of the wave at some instant in time The blue curve is later in time The high points are crests of the wave The low points are troughs of the wave

17. Interference of Sound Waves Sound waves interfere Constructive interference occurs when the path difference between two waves’ motion is zero or some integer multiple of wavelengths path difference = mλ Destructive interference occurs when the path difference between two waves’ motion is an odd half wavelength path difference = (m + ½)λ

18. Mathematical Representation It can be derived by comparing the factors of x and t, that and Dividing  and k gives v, that is A wave moves to the left with velocity v and wave length, can be described using

19. Doppler Effect If the source is moving relative to the observer The doppler effect is the change in frequency and wavelength of a wave that is perceived by an observer when the source and/or the observer are moving relative to each other. http://en.wikipedia.org/wiki/Doppler_effect

20. 19. INTERFERENCE Light waves interfere with each other much like mechanical waves do Constructive interference occurs when the paths of the two waves differ by an integer number of wavelengths (  x=m ) Destructive interference occurs when the paths of the two waves differ by a half-integer number of wavelengths (  x=(m+1/2) )

21. Interference Equations The difference in path difference can be found as  x = d sinθ For bright fringes, d sinθ bright = mλ, where m = 0, ±1, ±2, … For dark fringes, d sinθ dark = (m + ½) λ, where m = 0, ±1, ±2, … The positions of the fringes can be measured vertically from the center maximum, y  L sin θ (the approximation for little θ)

22. Single Slit Diffraction A single slit placed between a distant light source and a screen produces a diffraction pattern It will have a broader, intense central band The central band will be flanked by a series of narrower, less intense dark and bright bands

23. Single Slit Diffraction, 2 The light from one portion of the slit can interfere with light from another portion The resultant intensity on the screen depends on the direction θ

24. Single Slit Diffraction, 3 The general features of the intensity distribution are shown Destructive interference occurs for a single slit of width a when asinθ dark = mλ m =  1,  2,  3, …

25. Interference in Thin Films The interference is due to the interaction of the waves reflected from both surfaces of the film Be sure to include two effects when analyzing the interference pattern from a thin film Path length Phase change

26. Facts to Remember The wave makes a “round trip” in a film of thickness t, causing a path difference 2nt, where n is the refractive index of the thin film Each reflection from a medium with higher n adds a half wavelength /2 to the original path The path difference is  x = x 2  x 1 For constructive interference  x = m For destructive interference  x = (m+1/2) where m = 0, 1, 2, … Path change x 1 = /2 Path change x 2 = 2nt

27. Thin Film Summary Low  x = 2nt  /2 n x 1 = /2 x 2 = 2nt High Low  x = 2nt n x 1 = 0 p 2 = 2nt Low High  x = 2nt n x 1 = /2 x 2 = 2nt+ /2 High  x = 2nt + /2 n x 1 = 0 x 2 = 2nt + /2 Thinnest film leads to constructive 2nt = destructive 2nt = /2 Thinnest film leads to constructive 2nt =  destructive 2nt =

28. 20. COULOMB’S LAW Coulomb shows that an electrical force has the following properties: It is along the line joining the two point charges. It is attractive if the charges are of opposite signs and repulsive if the charges have the same signs Mathematically, k e is called the Coulomb Constant k e = 9.0 x 10 9 N m 2 /C 2

29. Vector Nature of Electric Forces The like charges produce a repulsive force between them The force on q 1 is equal in magnitude and opposite in direction to the force on q 2

30. Vector Nature of Forces, cont. The unlike charges produce a attractive force between them The force on q 1 is equal in magnitude and opposite in direction to the force on q 2

31. The Superposition Principle The resultant force on any one charge equals the vector sum of the forces exerted by the other individual charges that are present. Remember to add the forces as vectors

32. Superposition Principle Example The force exerted by q 1 on q 3 is The force exerted by q 2 on q 3 is The total force exerted on q 3 is the vector sum of and