PHY 1371Dr. Jie Zou1 Chapter 38 Diffraction and Polarization

PHY 1371Dr. Jie Zou2 Outline Introduction to diffraction Diffraction from narrow slits Resolution of single-slit and circular apertures

PHY 1371Dr. Jie Zou3 Introduction to diffraction Diffraction: Waves bend or diffract, when they pass by a barrier or through an opening. The divergence of light from its initial line of travel is called a diffraction. Diffraction pattern

PHY 1371Dr. Jie Zou4 Diffraction from narrow slits: Observation Diffraction pattern of a single slit- observation: The pattern consists of a central bright fringe flanked by much weaker maxima alternating with dark fringes.

PHY 1371Dr. Jie Zou5 Diffraction of narrow slits: Explanation Explanation: According to Huygens’s principle, each portion of the slit acts as a point source of light waves. Light from one portion of the slit can interfere with light from another portion, and the resultant light intensity on a viewing screen depends on the direction .

PHY 1371Dr. Jie Zou6 Dependence of the resultant light intensity on direction  Large number of small zones, each with a width  y. Phase difference between adjacent zones:  = (2  / )  y sin  Total electric filed E at point P: E P =  Esin(  t) +  Esin(  t+  ) +…+  Esin(  t+N  ) It can be shown that: E P =(N  E)[sin(  /2)/(  /2)]sin(  t+  ), where  = N  = (2  / ) a sin . Light intensity at P: I = I max [sin(  /2)/(  /2)] 2. Assumption: The viewing screen is very far from the single slit.

PHY 1371Dr. Jie Zou7 Light intensity vs.  /2 plot For a single-slit diffraction, most of the light intensity is concentrated in the central bright fringe. Condition for intensity minima: sin  = m( /a), m =  1,  2,… The central maximum occurs at  = 0 (central point on the screen). To a good approximation, the secondary maxima lie midway between the zero points:  /2 =3  /2, 5  /2,…

PHY 1371Dr. Jie Zou8 Example 38.2 Relative intensities of the maxima Find the ratio of the intensities of the secondary maxima to the intensity of the central maximum for the single-slit diffraction pattern.

PHY 1371Dr. Jie Zou9 Resolution of single-slit and circular apertures The ability of optical systems to distinguish between closely spaced objects is limited because of the wave nature of light.

PHY 1371Dr. Jie Zou10 Rayleigh’s criterion for resolution Rayleigh’s criterion: When the central maximum of one image falls on the first minimum of the other image, the images are said to be just resolved. For a slit with width a, the limiting angle of resolution is:  min = /a. For a circular aperture of diameter D, the limiting angle of resolution is:  min = 1.22( /D).

PHY 1371Dr. Jie Zou11 Example 38.5 Resolution of the eye Estimate the limiting angle of resolution for the human eye, assuming its resolution is limited only by diffraction (Choose = 500 nm, and pupil diameter = 2 mm)

PHY 1371Dr. Jie Zou12 Homework Ch. 38, P. 1238, Problems: #1, 2, 18.