Physics II - Laser Interference Lab Notes | PH 113, Lab Reports of Advanced Physics

Download Physics II - Laser Interference Lab Notes | PH 113 and more Lab Reports Advanced Physics in PDF only on Docsity! PH 113 Laser Interference Lab MJM April 23, 2005 rev 2 Background You have already learned about interference r1 p of sound waves: waves starting in phase from s1 two sources s1 and s2 arriving at point p r2 will constructively interfere if the path diff- s2 erence is an integer number of wavelengths constructive interference (starting in phase): r = r1-r2 = integer  When the distance d between s1 and s2 is small compared to r1 or r2, the path difference can be approximated by (See text by Knight, Section 22.2, especially Fig 22.4, p. 688 ). p r1 s1 r2 y d s2 L  path difference = r2 - r1  d sin  . (The paths r1 and r2 are nearly parallel to each other.  can be taken as the angle of the x-axis to either path, or as the angle from the midpoint.) For angles which are 'small',   sin   tan  . (When  = 5.73o = 0.100 rad, sin  = 0.0988 and tan  = 0.1003.) In the sketch above, path difference  d sin  = d tan  = d (y/L) = m , where m = 0, 1, 2, etc. For a series of constructive interference points (loud points for sound waves, bright spots for light): (1) (d/L) y0 = 0  [this means ythis means y0 = 0] (d sin 0 = 0) (2) (d/L) y1 = 1  (d sin 1 = ) ... d/L ym = m . (d sin m = m ) If we take the difference y of any two of these ( m is the difference in m values ) we get (3) (d/L) y = m . In this experiment we will measure y values. For any y between bright spots it is easy to count m. Then if we know , we can calculate the separation d between the sources. Or if we know the separation d we can calculate the wavelength In your report: Write down several equations like (1), (2), for destructive interference. 1 Would we get a different equation (3) if we let y = distance between two dark spots ? Today's experiment. We'll use a helium-neon (He-Ne) laser putting out bright red light at a wavelength of 632.8 nm. This is in an aluminum box, and connects to the wall via a 12v wall plug. We'll also use a long glass bar containing a set of 1 to 5 adjacent slits, all the same width a and same spacing d. We'll try to observe and check a couple of features of light interference and diffraction. (See Knight, section 22.4) Laser (coherent) light through a single slit does not spread out uniformly in all directions, instead most of its light is concentrated in a small angle in the forward direction. A simple way of understanding this a is to assume many little sources of light are present in the slit. The sketch shows 8 beams of light headed off  from the slit to reach a distant point. Beam 1 is at the top and beam 8 at the bottom. If the angle is right for beam 5 to travel an extra half wavelength more than beam 1 it will cancel it out. If beam 5 cancels beam 1, then beam 2 will be cancelled by beam 6, 3 by 7 and beam 4 by beam 8. Then there would be no light at all, since total cancellation would occur. Since beam 1 and beam 5 are separated by a/2, the extra path between 1 and 5 would be a/2 sin . So for total cancellation of light from a single slit we would have (4) extra path between 1 and 5 = /2 = a/2 sin  (major dark spot from single slit diffraction) Single slit measurement. Tape a piece of paper to the wall and place a single slit in the HeNe laser beam. Record the distance L from the slit to the wall. Mark down the distance w (see p. 699) between the estimated location of the major dark spots on either side of the bright area. Then the angle  is obtained from (5) tan  = w/(2L) Calculate tan . Is it a 'small' angle? (Determine the angle  from the tangent. If  in radians is very close to the tangent, the angle is 'small'. Use Eq. (4) {  = a sin  }, helped out by Eq. (5) to calculate a, the width of a single slit. (Recall the HeNe wavelength is 632.8 nm). After lab, use uncertainties in w and L to estimate the uncertainty in the slit width a. 2