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Material Type: Notes; Class: Recitation for Lecture 001; Subject: Physics; University: George Mason University; Term: Unknown 1989;
Typology: Study notes
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adjacent minima is given by 2
2 cos d^ ^ 2 2 cos
cos d^ orN
Nd ^ ^
^ ^
^ Thus, for the small change in phase
, the angular position will change by,
sin^2 sin^2 N^ ^ ^ d^ 2
dor ^
^ ^
^
We also know how phase difference are related to the angular location
R Nm ^ Canceling the common factor
So, the resolving power of a diffraction grating increases by• using a grading with a larger number
N^ of lines
m
diffraction , light spreads out after passing thru smallapertures ^ this posses^ resolution limits
to commonly used optical instruments, such as microscopes and telescopes.
image will not be sharp
Rayleigh’s Criterion
which is similar in
spirit to our discussion for the resolving power for the diffraction grating:The two diffraction pattern will be resolvable if thecentral max from one pattern is at least as far as thest^1
min of the other image. For circular aperture with diameter
D , the location of the its 1
st^ order diffraction
minimum is:
sin 1.22 (^) 1 D (“1.22” is a geometric factor)
for a circular aperture is defined as the smallest angular separation between two light sources that can be resolved accordingto the^ Rayleigh’s Criterion
and it is given by:sin^ 1.22^ min
D
What is the minimum distance between twopoints on the object that one can resolve? f-number = f/D
^ D = f/f-number = 50mm/2 =25 mm Rayleigh’s Criterion gives:
9 5 min^ min^
500 103 sin^ 1.^
1.^ m^ 2.4^10 rad 25 10 D^
m
^ ^
^
^
' y y ' s s y^ y ^ separation of object points y’ ^ separation of the corresponding image points s ^ object distance s’ ^ image distance
y’ s
s’
