9.2 Diffraction Flashcards
What is diffraction?
The spreading of a wave as it foes through an aperture or past an obstacle.
What is the path difference between two light rays of identical wavelength?
(b/2)sin@ where b is the width of the slit. If the angle is very small this is approximately equal to b/2@ if the angle is expressed in radians.
What happens if the path difference is a half wavelength?
There will be destructive interference when the rays meet at the screen which is assumed to be at a long distance compared with the slit width. The same condition holds for a pair of rays from just below the top and just below the middle of the opening or indeed for any other such pair of rays at an angle @. The result will be a dark band at the screen at the diffraction angle
@D = lambda/b
What will happen to rays leaving the slit in a direction along the centre line where @=0?
They will arrive in phase and so there will be constructive interference and a bright band at the centre of the diffraction pattern.
What is the intensity of the first secondary maximum compared to the central maximum?
Around 4.5% of that of the central maximum.
What happens to the diffraction patter as the wavelength increases?
The width of the diffraction pattern increases.
If white light is incident on the slit what happens to the diffraction pattern?
Each constituent colour will have its own characteristic pattern and their combination will be a pattern which is white at the centre but coloured to the sides.
What does a detailed analysis of a diffraction pattern for a circular aperture diameter b show?
That the first diffraction minimum is observed at a diffraction angle of @D = 1.22(lambda/b)
What is resolution?
a measure of the ability of a detection device to distinguish two objects - to see them as separate objects.
What is the angular separation of light from two point sources that diffracts when they pass through an aperture separated by a distance s and distance d to the aperture?
@A = s/d
What happens if their separation is small enough?
The diffraction patterns of the two sources will overlap and the two sources may appear as one.
What is the Rayleigh Criterion?
Two sources are said to be just resolved if the central maximum of the diffraction pattern of one source falls on the first minimum of the other.
To satisfy the Rayleigh criterion what must the angular separation of the two sources be?
@A = @D = 1.22(lambda/b)
where b is the diameter of the circular aperture used to collect the light from the sources. So to know whether to sources are resolved we compare the angular separation @A and the diffraction angle.
What happens if the sources are not resolved?
@A < @D = 1.22(lambda/b)
What happens if the sources are just resolved?
The central maximum of one coincides with the first minimum of the other
@A = @D = 1.22(lambda/b)
