Question

a very fine wire ( 7.25 \times 10^{-3} ) mm in diameter is placed between two flat glass plates as in (figure 1). light whose wavelength in air is 640 nm falls (and is viewed) perpendicular to the plates and a series of bright and dark fringes are seen.

part a
how far apart are the dark fringes if the glass plates are each 20.5 cm long?
express your answer to three significant figures and include the appropriate units.
( delta x = ) value units

Explanation:

Step1: Identify the formula for fringe separation in air wedge

For an air wedge between two glass plates with a wire of diameter \( d \) at one end and length \( L \) of the plates, the fringe separation \( \Delta x \) is given by \( \Delta x=\frac{\lambda L}{2d} \), where \( \lambda \) is the wavelength of light, \( L \) is the length of the plates, and \( d \) is the diameter of the wire.

Step2: Convert units to consistent SI units

• Diameter \( d = 7.25\times 10^{-3}\space mm=7.25\times 10^{-6}\space m \) (since \( 1\space mm = 10^{-3}\space m \))
• Wavelength \( \lambda=640\space nm = 640\times 10^{-9}\space m \)
• Length \( L = 20.5\space cm=0.205\space m \) (since \( 1\space cm = 10^{-2}\space m \))

Step3: Substitute values into the formula

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Answer:

\( \Delta x = \boldsymbol{9.05\space mm} \) (or \( \boldsymbol{9.05\times 10^{-3}\space m} \))