Single Slits and Refraction

Question 1

Single Slit

Diffraction Pattern - Equation

Answer 1

-the diffraction pattern resulting from the light entering a single slit of width α displays minima at:
sinθ = mλ/α

α = width of slit

Question 2

Single Slit

Diffraction Pattern Explanation

Answer 2

• destructive interference occurs for dsinθ = (m+1/2)λ
• consider if the single wide slit was made up of many narrow slits
• the first minimum m=0 would occur when the light from the centre of the slit was out of phase with the light from the top of the slit
• the light from these two narrow slits at a distance α/2 from each other would interfere destructively
• it follows that the first minimum occurs when 1/2α=1/2λ so sinθ = λ/α

Question 3

Interference Diffraction From Two Slits

Answer 3

• if there are two or more finite slits the diffraction pattern is the product of the single slit and multiple slit patterns
• convolution of aperture functions leads to a product of diffraction patterns

Question 4

Franuhofer Diffraction

Answer 4

• observed far from the slits when rays are approximately parallel
• at very distant screnn spherical wavefronts tend to approximately planar and analysis becomes easier

Question 5

Fresnel Diffraction

Answer 5

• the diffraction pattern observed near to an aperture or obstacle
• rays cannot be considered parallel at this distance
• much more difficult to analyse than Fraunhofer
• as well as fringes you can still make out the objects shape

Question 6

Fraunhofer Diffraction Pattern of Circular Apertures

Equation

Answer 6

sinθ = 1.22 λ/D ≈ θ

θ = the angle subtended by the first diffraction minimum
λ = wavelength
D = diameter of the aperture

Question 7

Resolution of a Circular Aperture

Answer 7

• two stars, point sources of light, are imaged by a telescope with circular aperture of diameter, D
• each will produce a Fraunhofer diffraction pattern of the aperture, not a point image
• the resolution is how close together the two stars can be and still ne distinguishable / resolved in the image

Question 8

Rayleigh’s Criterion

Answer 8

• the images are just resolved when the central maxima of one image falls on the first minimum of the other
• closer together than this and the two sources are unresolved
• further apart and they are clearly separate in the image

Question 9

Rayleigh’s Criterion

Critical Angular Separation

Answer 9

αc = 1.22 λ/D

αc = critical angle
D = diameter of circular aperture

Question 10

Do waves travel in straight lines?

Particles

Answer 10

-particles will pass in a straight line through an aperture

Question 11

Do waves travel in straight lines?

Waves

Answer 11

• waves spread out from a small aperture, of size comparable to a wavelength
• this is the phenomenon of diffraction

Question 12

Ray Approximation

Answer 12

-when passing through an aperture much larger than the wavelength, waves travel approximately along straight lines

Question 13

Ray Approximation

Light

Answer 13

• often valid for light because most objects are large compared with visible wavelengths
• we notice that light usually travels in straight lines

Question 14

Ray Approximation

Sound

Answer 14

• often violated for sound because everyday objects are comparable to audible wavelengths
• we notice that sound is able to travel around corners

Question 15

Refractive Index

Answer 15

-a transparent medium is characterised by the index of refraction or refractive index, n
n = c/v

n = refractive index
c = speed of light in a vacuum
v = speed of light in the medium

Question 16

Refractive Index of Water

Answer 16

1.33

Question 17

Refractive Index of Air

Answer 17

1.0003

Question 18

Refractive Index of Diamond

Answer 18

2.4

Question 19

Snell’s Law of Refraction

Answer 19

-when a light ray crosses an interface between two media of refractive indices n1 and n2, the angles (relative to the normal) of the incident and refracted rays are as follows:
n1 sinθ1 = n2 sinθ2