Overview of Light Properties, Thin Lenses, and Wave Motion for Physics Midterm Exam

1. University Physics Midterm Exam Overview

2. 16. THE NATURE OF LIGHT • Speed of light c = 3x108 m/s (in the vacuum) v = c/n (in the media) • Formulas c = lf = l/T , 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 • n1 sin θ1 = n2 sin θ2 • θ1 is the angle of incidence • θ2 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 (lmed=l/n) do change

6. 17. THIN LENSES Thin Lens Equation Magnification

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 • m 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 A wave moves to the left with velocity v and wave length l, can be described using It can be derived by comparing the factors of x and t, that and Dividing w and k gives v, that is

19. Doppler Effect • If the source is moving relative to the observer • The doppler effectis 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 (Dx=ml) • Destructive interference occurs when the paths of the two waves differ by a half-integer number of wavelengths (Dx=(m+1/2)l)

21. Interference Equations • The difference in path difference can be found as Dx = d sinθ • For bright fringes, d sinθbright = mλ, where m = 0, ±1, ±2, … • For dark fringes, d sinθdark = (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 asinθdark = 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 Path change x1 = l/2 Path changex2 = 2nt • 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 l/2 to the original path • The path difference is Dx = x2 x1 • For constructive interferenceDx = ml • For destructive interferenceDx = (m+1/2)l where m = 0, 1, 2, …

27. Dx = 2nt + l/2 Dx = 2nt l/2 Dx = 2nt Dx = 2nt x1 = l/2 x1 = l/2 x1 = 0 x1 = 0 x2 = 2nt + l/2 x2 = 2nt+l/2 p2 = 2nt x2 = 2nt Low High Low High n n n n Low High Low High Thin Film Summary Thinnest film leads to constructive 2nt = l destructive2nt = l/2 Thinnest film leads toconstructive 2nt = l/2 destructive2nt = l

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, • ke is called the Coulomb Constant • ke = 9.0 x 109 N m2/C2

29. Vector Nature of Electric Forces • The like charges produce a repulsive force between them • The force on q1 is equal in magnitude and opposite in direction to the force on q2

30. Vector Nature of Forces, cont. • The unlike charges produce a attractive force between them • The force on q1 is equal in magnitude and opposite in direction to the force on q2

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 q1 on q3 is • The force exerted by q2 on q3 is • The total force exerted on q3 is the vector sum of and