Waves and OpticsWaves and OpticsNisha Issac (: & Ethan MunguiaNisha Issac (: & Ethan Munguia

InterferenceInterference

When two waves pass through the same When two waves pass through the same region of space at the same timeregion of space at the same time

2 types: 2 types: Constructive: crest to crest; larger amplitudeConstructive: crest to crest; larger amplitudeDestructive: crest to trough; resultant is zero if Destructive: crest to trough; resultant is zero if

both the waves have same amplitude.both the waves have same amplitude.

DiffractionDiffraction

Refers to the ability of waves to bend Refers to the ability of waves to bend around obstacles around obstacles

Amount of diffraction depends on the Amount of diffraction depends on the wavelength of the waves and the size of wavelength of the waves and the size of the obstacle. the obstacle.

In the case of narrow opening, the amount In the case of narrow opening, the amount of bending increases as the size of the of bending increases as the size of the opening decreases.opening decreases.

Dispersion of lightDispersion of light

Spreading of white lightSpreading of white lightDispersion of light in a transparent Dispersion of light in a transparent

material occurs because the index of material occurs because the index of refraction of the material varies the refraction of the material varies the wavelength.wavelength. Index of refraction is higher for shorter Index of refraction is higher for shorter

wavelengthswavelengths

Electromagnetic SpectrumElectromagnetic Spectrum

Radio waves, Microwaves, Infrared, Radio waves, Microwaves, Infrared, Ultraviolet, X-Rays, Gamma RaysUltraviolet, X-Rays, Gamma Rays

ReflectionReflection

““Bouncing” off of a wave of a surface; Bouncing” off of a wave of a surface; exact angleexact angle

Angle of incidence = Angle of reflectionAngle of incidence = Angle of reflectionThe angle of incidence is the angle that The angle of incidence is the angle that

light is striking a surface. The angle of light is striking a surface. The angle of reflection is the angle that the light is reflection is the angle that the light is reflected, or bouncedreflected, or bounced

RefractionRefraction

Change in direction of a wave when it passes Change in direction of a wave when it passes into a new substanceinto a new substance

Reason it changes direction or bends is because Reason it changes direction or bends is because each different substance has its own effect on each different substance has its own effect on speed of light.speed of light.

Index of refraction- Equals the ratio of speed of Index of refraction- Equals the ratio of speed of light in a vacuum to the speed of light in a light in a vacuum to the speed of light in a transparent substance. Determines the angle of transparent substance. Determines the angle of bending of the light at the interface between two bending of the light at the interface between two transparent substances. transparent substances.

MirrorsMirrors

Reflective surfacesReflective surfacesConvex and Concave Convex and Concave Has a focal point, where all the light Has a focal point, where all the light

directed at that mirror converges or directed at that mirror converges or diverges and the distance between the diverges and the distance between the mirror and that point is the focal length. mirror and that point is the focal length.

LensesLenses

Has a focal point Has a focal point Focal point of the lens- point where rays Focal point of the lens- point where rays

parallel and very close to the principal axis parallel and very close to the principal axis all pass through after refraction by the all pass through after refraction by the lens.lens.

Focal Length- distance from the center of Focal Length- distance from the center of lens to focal pointlens to focal point

Radius of curvature of a lens is exactly Radius of curvature of a lens is exactly twice the focal length. twice the focal length.

Important FormulasImportant Formulas

θθ = the angle of spread of a wave after passing = the angle of spread of a wave after passing through a single slit openingthrough a single slit opening

λ λ = wavelength= wavelength fn fn = the = the nthnth frequency in a series of resonant frequency in a series of resonant

frequenciesfrequencies v v = speed of the wave= speed of the wave LL = length = length DD = width of an opening through which a wave = width of an opening through which a wave

will diffractwill diffract

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Example #1

A ray of light strikes the surface of a flat glass plate at an incident angle of 30(degree). The index of refraction of air and glass are 1.00 and 1.50, respectively. Determine the a) angle of reflection and b) angle of refraction.

Answer: The reflected ray follows the laws of specular

reflection and so the angle of reflection is 30 degrees Snell’s law; 19 degrees

Example #2

A laser beam is incident on 2 slits separated by .500mm. The interference pattern is formed on a screen 1.00m from the slits & the 1st fringe is found to be .120cm to the right of the central maximum. A) Calculate the wavelength of the light in nm & b) determine the maximum number of bright fringes that can be observed.

Answers: A: 6.00 x 10-7

B: m=833

Example #3

A radar pulse travels from Earth to the moon & back in 2.60 secs. Calculate the distance from the Earth to the moon in a) meters and b) in miles

Answers:d= 3.90 x 108 md= 2.42 x 105 miles