In a double slit experiment, a very thin plate of glass of refractive index 1.58 is placed in the light path of one of the slit beams. When this was done, the center of the fringe pattern was displaced by 35 fringe widths. Calculate the thickness of the glass plate if the wavelength of light is 680 nm. A) 4.1 × 10^-⁵ m B) 1.5 × 10^-⁵ m C) 3.0 × 10^-⁵ m D) 8.2 × 10^-⁵ m E) 3.8 × 10^-⁵ m

Question

Quizplus · Accepted Answer

The displacement of the fringe pattern is given by:$$x = \frac{d\lambda}{D} \left(n_g - 1 ight)$$where:* x is the displacement of the fringe pattern* d is the distance between the slits* \lambda is the wavelength of light* D is the distance between the slits and the screen* n_g is the refractive index of the glass plateIn this problem, we are given:* x = 35 fringe widths* d = 0.1 mm* \lambda = 680 nm* D = 1 m* n_g = 1.58Substituting these values into the equation, we get:$$35 imes 0.1 imes 10^{-3} = \frac{0.1 imes 680 imes 10^{-9}}{1} \left(1.58 - 1 ight)$$$$3.5 imes 10^{-3} = 6.8 imes 10^{-12} \left(0.58 ight)$$$$3.5 imes 10^{-3} = 3.94 imes 10^{-12}$$$$t = \frac{3.5 imes 10^{-3}}{3.94 imes 10^{-12}} = 4.1 imes 10^{-5} ext{ m}$$Therefore, the thickness of the glass plate is 4.1 × 10^-⁵ m.

In a Double Slit Experiment, a Very Thin Plate of Glass