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You place one glass slide on top of another, with an animal hair between them at one end. You illuminate the slides with blue light of wavelength You count along the slide and find 300 transitions from bright to dark and back to light. How thick is the hair?
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Understand that the problem involves interference patterns created by thin film interference, where the hair acts as a wedge between the two glass slides.
Recognize that each transition from bright to dark or dark to bright corresponds to a change in the path difference of half a wavelength (λ/2) of the light used.
Given that there are 300 transitions, calculate the total path difference by multiplying the number of transitions by half the wavelength: Total path difference = 300 * (450 nm / 2).
The total path difference is also equal to twice the thickness of the hair (since light travels down and back up through the thickness of the hair), so set up the equation: 2 * thickness = Total path difference.
Solve for the thickness of the hair by dividing the total path difference by 2, and convert the result from nanometers to micrometers for the final answer.