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Chapter 34: Problem 70

A glass with a refractive index of 1.50 is inserted into one arm of a Michelson interferometer that uses a 600.-nm light source. This causes the fringe pattern to shift by exactly 1000 fringes. How thick is the glass?

Short Answer

Expert verified
Answer: The thickness of the glass plate is 600 µm.

Step by step solution

01

1. Write down the given values

We have been given the following information: - Refractive index of glass, n = 1.50 - Wavelength of light source, λ = 600 nm - Fringe shift observed, Δ𝑓 = 1000 fringes
02

2. Formula for path difference

The path difference has a direct relationship with the fringe shift observed. For the given fringe shift, we can use the following formula for path difference: Δd = λ * Δf
03

3. Calculate path difference

Now using the given values, let's calculate the path difference due to the glass plate: Δd = (600 nm) * (1000 fringes) = 600,000 nm
04

4. Formula for thickness using refractive index

When a glass plate is inserted in the path, the light travels an additional distance through the glass plate. And the extra distance is related to the refractive index and thickness of the glass. The extra path difference can be given by: Δ𝑑 = 2 * (n-1) * t where t is the thickness of the glass plate.
05

5. Solve for thickness

Now, we can solve the above equation for the thickness (t) of the glass plate: t = Δ𝑑 / 2 * (n-1) t = (600,000 nm) / (2 * (1.50 - 1)) t = 600,000 nm / 1 = 600,000 nm
06

6. Convert the thickness to a suitable unit

Finally, let's convert the thickness to a more suitable unit such as micrometers: t = 600,000 nm * (1 µm / 1,000 nm) = 600 µm Therefore, the thickness of the glass plate inserted in the Michelson interferometer is 600 µm.

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Most popular questions from this chapter

34.35 Monochromatic blue light \((\lambda=449 \mathrm{nm})\) is beamed into a Michelson interferometer. How many fringes move by the screen when the movable mirror is moved a distance \(d=\) \(0.381 \mathrm{~mm} ?\)

In a double-slit experiment, He-Ne laser light of wavelength \(633 \mathrm{nm}\) produced an interference pattern on a screen placed at some distance from the slits. When one of the slits was covered with a thin glass slide of thickness \(12.0 \mu \mathrm{m},\) the central fringe shifted to the point occupied earlier by the 10 th dark fringe (see figure). What is the refractive index of the glass slide? (a) Without the glass slide (b) With glass slide

What is the wavelength of the X-rays if the first-order Bragg diffraction is observed at \(23.0^{\circ}\) related to the crystal surface, with inter atomic distance of \(0.256 \mathrm{nm} ?\)

The thermal stability of a Michelson interferometer can be improved by submerging it in water. Consider an interferometer that is submerged in water, measuring light from a monochromatic source that is in air. If the movable mirror moves a distance of \(d=0.200 \mathrm{~mm},\) exactly \(N=800\) fringes move by the screen. What is the original wavelength (in air) of the monochromatic light?

Coherent, monochromatic light of wavelength \(450.0 \mathrm{nm}\) is emitted from two locations and detected at another location. The path difference between the two routes taken by the light is \(20.25 \mathrm{~cm}\). Will the two light waves interfere destructively or constructively at the detection point?
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