3B Chapter 18

phase shift of light wave

phase shift of pi rad if it reflects from a boundary at which the index of refraction increases

• no phase shift at a boundary where the index of refraction decreases

path-length difference: constructive interference

2nt = (m +1/2)λ; m = 0,1,2…

phase difference: destructive interference

2nt = mλ; m = 0,1,2

phase shift: neither or both reflected waves undergo a phase shift

△x = 2t

• phase shifts cancel

phase shift: only one wave undergoes a phase shift

△x = 2t + 1/2λ

when the constructive or destructive waves are equal to 2nt

when both wavelengths are in the air

angle of bright fringes for double-slit interference

dsinθ = mλ; m = 0,1,2,3

y = Lsinθ

what is the thickness of an optical caoting of MgF2 whose index of refraction is n=1.38 and which is designed to eliminate reflected light at wavelengths (in air) around 550 nm when incident normally on glass for which n=1.50?

2nt = (m+1/2)λ

The color is produced by a 330 nm thick layer of keratin (n=1.56) with air on both sides that is found around the edge of the feather barbules. what wavelength(s) of visibly light are strongly reflected by this structure?

constructive; 2nt = (m+1/2)λ

m = 0, 1, 2

two narrow slits are illuminated by light of wavelength. the slits are spaced 20 wavelengths apart. what is the angle, in rads, between the central maximum and the m=1 bright fringe?

m = 1

dsinθ = λ

white light passes thru two slits 0.5 mm apart, and an interference pattern is observed on a screen 2.5 m away. the first-order fringe resembles a rainbow with violet and red light at opposite ends. the violet light is about 2.0 mm and the red 3.5 mm from the center of the central white fringe. estimate the wavelengths for the violet and red light

dsinθ = λ = dy/L

light of wavelength 620 nm illuminated a diffraction grating. the second-order maximum is at angle 39.5. how many lines per mm does this grating have?

dsinθ = mλ; m=2; θ = 39.5
N = 1E-2 / d

determine the angular positions of the first and second-order maxima for light of wavelength 400 nm and 700 nm incident on a grating containing 10,000 lines/cm

d = (1E-2)/10,000 = 1E-6

dsinθ = mλ

m = 1 and 2

huygen’s principle

1. each point a wave front is the source of a spherical wavelet that spreads out at the wave speed

2. at a later time, the shape of the wave front is the curve that is tangent to all the wavelets

width of central maximum

w = (2λL)/a

a beam of monochromatic green light is diffracted by a slit of width 0.55 mm. the diffraction pattern forms on a wall 2.06 m beyond the slit. the distance between the positions at 0 intensity on both sides of the central bright fringe is 4.10 mm. calculate the wavelength of the light.

λ = (wa)/2L

circular aperature diffraction

θ = 1.22λ/D

w = 2.44λL/D

light from a helium-neon laster (λ = 633 nm) passes thru a circular aperature and is observed on a screen 4 m behind the aperture. the width of the central maximum is 2.5 cm. what is the diameter in mm of the hole?

D = 2.44λL / w

circular aperatures with limtis of resolution

θ = 1.22λ/D

you are in a plane at an altitude of 10,000 m. if you look down at the ground, estimate the minimum sparation s between objects that you could distinguish. could you count cars in a parking lot? consider only diffraction, and assume ur pupil si about 3 mm in diameter and λ = 550 nm

△x = L(1.22λ/D)