1200 HALL, LIND AND RISTINEN spectrum becomes badly nonlinear. This would ACKNOWLEDGMENTS indicate that the discriminator is probably trig- The assistance of Mr Harry Clark in machining gering due to meaningless noise from the photo- the scintillator plastic and the help of several multiplier tube at these low settin other staff members in the development of this IV SUMMARY apparatus is sincerely appreciated This experiment performs well and is simple *Equipment provided in part by a enough to be used in an undergraduate physics lab. With some care given to least squares methods (Academic, New York, 1967) of data analysis and accurate time calibration, it B. Rossi, High Energy Particles(Prentice-Hall, is capable of producing research quality data. Englewood Cliffs, N.J., 1952) AMERICANJOURNAL OF PHYNICS VOLUME 38, NUMBER 10 Visual appearance of a Moving Vertical Line RAMESH BHANDARI Physics Department, Panjab University, Chandigarh, India (Received 2 March 1970; revision received 19 May 1970) a vertical line moving with velocity 1, when seen, assumes the shape of a hyperbola or para- bola accordingly as v <c or v=c. At v>c, which actually is not possible, the line takes the form of an ellipse or parts of an ellipse, or even becomes imaginary, depending upon the length of the line, the magnitude of the velocity, and the distance of the viewer from the line. If, however, a line moving with v<c recedes from the viewer, it seems less curved until at in finity it straightens up to look vertical again In this paper, I have dealt in detail with the of all points lying on the line, the light rays from of ng vertical line and the which, emitted at different instants(At), arrive subsequent changes that take place in it with the at P simultaneously. It is similar to the standard passage of time equation! of a hyperbola in the az plane, drawn Consider a line coincident with the 2 axis of a with the origin shifted to (rl, y ) To the viewer frame moving with velocity v as shown in Fig. 1. therefore, the line looks like a hyperbola with The light ray I from end 0 reaches the viewer's focus F=[y/(1+B),0] and directrix D given by eye fixed in the laboratory frame at(O, y, 0) after a time interval y/c. The ray II from A,on x=-8y/(1+β); the other hand arrives at P at the same time as y here is a constant. The eccentricity e is a funetion after being emitted at an earlier instant At. of v and is equal to 1/ From the figure, it is clear that DEPENDENCE OF APPEARANCE ON D c△+y=[(v△)2+y2+22]/ Atv=0, e=0o. F tends to(, 0) and the di- Multiplying both sides by v/c and squaring the rectrix coincides with the z axis. The hyperbol resulting expression, we arrive at the equation consequently, straightens up coinciding with the x2(1-B2)+2X6y-B22=0 2 axis. However, when the line moves with a finite velocity v<c, it assumes the shape of a hyperbola where X=vAt. This can be further put in the form and at v=c transforms into a parabola given by [(X+B2y)/(8?2y)2]-[Z/(y)2]=1.(3) Equation(3)is in fact the equation of the locus It is interesting to note that with further increase