Question from my assignment

Question

Two plane glass plates are placed on top of one another and on side a paper is introduced to form a thin wedge of air. assuming that a beam of wavelength 600 nm is incident normally, and that there are 100 interference fringes per cm, calculate the wedge angle.

Answer 1

The place where the two plates come in contact produces a dark fringe and that leaves 99 along the 1cm plate of glass. So The separation distance is calculated as d= 99(λ/2) and using the information in the problem gives d= 2.97x10^-5 m. The wedge angle can be calculated as tanθ =d/10^-2 = 2.97x10^-3 Taking the tan^-1 (2.97x10^-3) gives θ =.17°.

Answer 2

In this sort of configuration, with near-normal incidence (assumed to be normal, because even though the plates are at an angle to each other, the angle is so small that light entering the wedge gap perpendicular to one side is basically perpendicular to the other), every fringe -- presumed bright -- represents a change in the thickness of the gap by one wavelength.

Therefore, going 1 cm along the direction of the gap, its thickness change by 100 wavelengths (100 fringes per cm). If we start at the apex of the wedge, where the plates touch, then the plates will be 100 wavelengths apart in 1 cm along the gap. 100 wavelengths is 100(600 nm) = 60000 nm or 0.06 mm. Since this is much, much smaller than 1 cm (= 10 mm), we are validated in our assumption that the wedge angle is very small.

So we can calculate the angle (in radians) using:

θ = (x/r)

where x = 0.06 mm

r = 10 mm

If you have any questions, about this, please let me know. Good luck!

NOTE: This assumes 100 fringes means 100 orders. If 100 fringes means 50 light, 50 dark, then multiply the wavelength by 50 instead of 100. The contact point does not count as a fringe, as there is no interference there (since there is no path difference), and the first fringe in the gap will be a bright one.