Two extremely flat glass plates,10.0 cm wide,touch at one end but are separated by a thin wire at the other end,forming a wedge.Light with a wavelength of 450 nm shines almost perpendicularly on the glass and forms fringes which are 1.80 mm apart.What is the diameter of the wire?
A) 25.0 µm
B) 17.5 µm
C) 20.0 µm
D) 12.5 µm
E) 10.0 µm

Question

Quizplus · Accepted Answer

The distance between the fringes (Δy) is given by:
Δy = λL/d
where λ is the wavelength of light, L is the length of the glass plates, and d is the distance between the wire and the plates.
Solving for d, we get:
d = λL/Δy = (450 x 10^-9 m) x (10^-1 m) / (1.80 x 10^-3 m) = 2.5 x 10^-5 m

The diameter of the wire (D) can be calculated using trigonometry:
tanθ = D/2d
where θ is the angle of the wedge formed by the plates.
Assuming a small angle approximation, we have:
tanθ ≈ θ = Δy/L
Substituting the given values, we get:
θ ≈ 1.80 x 10^-3 m / 10^-1 m = 1.8 x 10^-2 rad
Therefore,
D = 2dtanθ = 2 x 2.5 x 10^-5 m x tan (1.8 x 10^-2 rad) ≈ 1.25 x 10^-5 m
D ≈ 12.5 µm

Therefore, the best choice is D which is 12.5 µm in diameter.

Two Extremely Flat Glass Plates,10