Diffraction and Resolution - Union...
Transcript of Diffraction and Resolution - Union...
Diffraction and Resolution
� Fraunhofer Diffraction Pattern of a Single Slit
� Resolution of Single-Slit and Circular Apertures
� The Diffraction Grating
� Homework
Fraunhofer Diffraction - Qualitative
� Each part of the slit acts as a source of waves.
� Light from one part of the slit can interfere with light fromanother part.
� The resulting intensity on the screen depends on the angle�.
Fraunhofer Diffraction - Quantitative
� If we divide the slit into two parts, waves from the upper halfinterfere destructively with waves from the lower half when�
������ � � � �� ����� � � �
� If we divide the slit into four parts, we get
����� � � ��
Fraunhofer Diffraction - Quantitative (Continued)
� If we divide the slit into six parts, we get
����� � � ��
� Therefore, the general condition for destructive interference is
���� ���������� � � �� � � ��� � � �!� � �#"$"#"&%
Single-Slit Diffraction Example
A slit of width � is illuminated by red light of wavelength � = 650nm. For what value of � will the first minima appear at
�= 15 ' ?
Single-Slit Diffraction Example
A slit of width � is illuminated by red light of wavelength � = 650nm. For what value of � will the first minima appear at
�= 15 ' ?
���� � � � �
� � ������ � � �(% �*)�+�,.- � %
����� � + ' � + �/� - � � " +10 �
Resolution of Small Apertures
� Two point sources far from the aperture each produce a diffrac-tion pattern.
� If the angle subtended by the sources at the aperture is largeenough, the diffraction patterns are distinguishable as shownin Fig. (a).
� If the angle is small, the diffraction patterns can overlap so thatthe sources are not well resolved as shown in Fig. (b).
Condition of Resolution
� The limiting condition of resolution is know as Rayleigh’s cri-terion.
� When the central maximum of the diffraction pattern of onesource falls on the first minimum of the diffraction pattern ofanother source, the sources are said to be resolved.
� We found that the first minimum in a single-slit diffractionpattern occurs when
����� � � �
� Therefore, the limiting angle of resolution (in radians) for aslit of width a is �$24365 � �where we have applied the small angle approximation ����� �87 �
Resolution for a Circular ApertureThe limiting angle of resolution for a circular aperture of diameter9
is � 24365 �/" �/� �9
Well resolved
Just resolved
Not resolved
The Diffraction Grating
� For light incident normally on the plane of the grating withspacing d, the condition for maxima is: ����� ��;<� 3>=�?A@ � � � � , �#��� � �$"#"$">%
Diffraction Grating Interference Pattern
Homework Set 3 - Due Mon. Apr. 5
� Read Sections 27.6 - 27.8
� Answer Questions 27.14 & 27.22� Do Problems 27.19, 27.26, 27.29 & 27.32