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What is the width of the central bright fringe

(TO SUBMIT BEFORE 06/12/2010)
1/ (20 pts) Red light of wavelength 633 nm from a helium-neon laser passes through a slit 0.350 mm
wide. The diffraction pattern is observed on a screen 3.00 m away.
Define the width of a bright fringe as the distance between the minima on either side.
(a) What is the width of the central bright fringe?
(b) What is the width of the first bright fringe on either side of the central one?
2/ (20 pts) Consider a particle moving in one dimension, which we shall call the x-axis.
(a) What does it mean for the wave function of this particle to be normalized?
(b) If the particle described by the wave function ψ ( x) = Aebx , where A and b are positive real numbers,
is confined to the range x ≥ 0 , determine A (including its units) in function of b so that the wave
function is normalized.
3/ (20 pts) (a) The x-coordinate of an electron is measured with an uncertainty of 0.20 mm. What is the
x-component of the electron's velocity, vx , if the minimum percentage uncertainty in a simultaneous
measurement of vx is 1.0%?
(b) Repeat part (a) for a proton. The mass of proton is 1.67 ×10−27 kg .
4/ (20 pts) Consider a particle in a box with rigid walls at x = 0 and x = L. Let the particle be in the first
2 2πx sin ÷.
(a) For which values of x, if any, in the range from 0 to L is the probability of finding the particle zero?
(b) For which values of x is the probability highest?
5/ (20 pts) Two thin converging lenses of focal lengths f1 = 10.0 cm and
f2 = 20.0 cm and are separated by 20.0 cm, as illustrated in Figure 1. An
object is placed 15.0 cm to the left of lens 1. Find the position of the
final image and the magnification of the system.
excited level and use the corresponding wave function ψ 2 (x) = THE END
Figure 1

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