Phasors and Multiple Slits

Question 1

Phasor

Definition

Answer 1

-vectors with direction defined by the field’s phase

Question 2

Phasor Diagram

Answer 2

E1 = E0 sin(ωt)

• an arrow of length E0 drawn from the origin
• ωt is the angle measured anticlockwise between the vector and the positive x axis
• E1 is the phasors projection onto the vertical axis

Question 3

Phasor Diagram

Superposition

Answer 3

E1 = E0 sin(ωt)
E2 = E0 sin(ωt+𝛿)
-E2 is drawn from the end of E1, with length E0 and at an angle 𝛿 further anticlockwise than E1
-the amplitude and phase of E1+E2 are given by a vector sum of the two phasorrs
-Er is the resultant phasor and is a straight line from the beginning of E1 to the end of E2
-Etot is the projection of Er onto the vertical axis
-the whole phasor diagram rotates at rate ω but its relative geometry remains unchanged as phase differences are constant

Question 4

How are Etot and Er related?

Answer 4

Er is the amplitude of Etot

Question 5

3 Slits - Field at P

Answer 5

-the field at P is a superposition of
E1 = E0 sin(ωt)
E2 = E0 sin(ωt+ϕ)
E3 = E0 sin(ωt+2ϕ)

Question 6

3 Slits - First Order Minimum

Answer 6

ϕ = 2π/3
Δ = λ/3

Question 7

3 Slits - First Order Small (secondary) Maximum

Answer 7

ϕ = π
Δ = λ/2

Question 8

3 Slits - Second Order Minimum

Answer 8

ϕ = 4π/3
Δ = 2λ/3

Question 9

3 Slits - First Order Primary Maxima

Answer 9

ϕ = 2π
Δ = λ

Question 10

More Slits

Answer 10

-on increasing the number of equally spaced slits, primary maxima remain fixed at
sin θ = mλ/d
-but maxima get narrower and brighter
-secondary maxima increase in number but fade away

Question 11

Diffraction Grating

Description

Answer 11

• composed of a large number of equally spaced parallel slits
• typically hundreds to thousands of lines per mm to improve resolution
• bright, sharp maxima appear

Question 12

Diffraction Grating

Uses

Answer 12

-to measure the wavelength of light
-fringe spacing depends of λ
Ym+1 - Ym = λL/d

Question 13

Diffraction Grating

Equation

Answer 13

d sin θ = mλ

where m is an integer

Question 14

Diffraction Grating

Green Light

Answer 14

-equally spaced green maxima

Question 15

Diffraction Grating

White Light

Answer 15

-central white maximum
-other maxima are a rainbow
-the higher the order of the maximum, the more spread out the light is
-colours from different orders can overlap since
d sin θ = mλ
-this occurs when
m1λ1 = m2λ2