Final answer:
The lower and upper limits on the hair's diameter can be determined using the interference pattern produced by the two glass plates and the hair. The thickness of the hair is found to be 1.44 x 10^(-4) cm. The lower limit of the hair's diameter is 2.88 x 10^(-4) cm and the upper limit is 3.229 x 10^(-4) cm.
Step-by-step explanation:
The lower and upper limits on the hair's diameter can be determined by considering the interference pattern produced by the two glass plates and the hair. When illuminated with a sodium lamp with a wavelength of 589nm, the hair is observed between the 180th and 181st dark fringes.
The distance between consecutive fringes in the interference pattern can be calculated using the formula:
d = λL / (2t)
Where d is the distance between fringes, λ is the wavelength of light, L is the distance between the glass plates, and t is the thickness of the hair. By rearranging the formula, we can solve for t:
t = λL / (2d)
Substituting the given values, we have:
t = (589nm)(7.50cm) / [(2)(181 - 180)] = 1.44 x 10^(-4) cm
This represents the thickness of the hair. To determine the diameter, we can assume the hair is cylindrical. Therefore, the lower limit of the hair's diameter is twice the calculated thickness, and the upper limit is twice the thickness plus the diameter of the copper wire (29.45 μm).
Lower limit = 2(1.44 x 10^(-4) cm) = 2.88 x 10^(-4) cm
Upper limit = 2(1.44 x 10^(-4) cm) + 29.45 μm = 2.88 x 10^(-4) cm + 2.945 x 10^(-3) cm = 3.229 x 10^(-4) cm