Question

ou are using a hydrogen discharge tube and high quality red and blue light filters as the light source for a Michelson interferometer. The hydrogen discharge tube provides light of several different wavelengths (colors) in the visible range. The red light in the hydrogen spectrum has a wavelength of 656.3 nm and the blue light has a wavelength of 434.0 nm. When using the discharge tube and the red filter as the light source, you view a bright red spot in the viewing area of the interferometer. You now move the movable mirror away from the beam splitter and observe 146 bright spots. You replace the red filter with the blue filter and observe a bright blue spot in the interferometer. You now move the movable mirror towards the beam splitter and observe 122 bright spots. Determine the final displacement (include sign) of the moveable mirror. (Assume the positive direction is away from the beam splitter.)

Answer 1

To find the final displacement of the moveable mirror in a Michelson interferometer, we calculate the distances moved for each wavelength based on the number of observed bright spots for red and blue light, then subtract the blue displacement from the red displacement taking their directions into account.

Step-by-step explanation:

To determine the final displacement of the moveable mirror in a Michelson interferometer experiment, we first calculate the distance moved for each wavelength of light based on the number of bright spots (interference fringes) observed.

For the red light with a wavelength of 656.3 nm, the mirror was moved away from the beam splitter, resulting in 146 bright spots. Since each bright spot corresponds to a half-wavelength shift, the total distance moved is:

Distance (red) = Number of fringes × Wavelength / 2 = 146 × 656.3 nm / 2

For the blue light with a wavelength of 434.0 nm, the mirror was moved towards the beam splitter, observing 122 bright spots. The distance the mirror was moved towards the beam splitter is:

Distance (blue) = Number of fringes × Wavelength / 2 = 122 × 434.0 nm / 2

To find the net displacement, we subtract the blue light distance from the red light distance. Note that the red displacement is positive because the mirror moved away from the beam splitter, and the blue displacement is negative because the mirror moved towards the beam splitter. Therefore:

Net Displacement = Distance (red) - Distance (blue)

This value represents the final displacement of the moveable mirror in the Michelson interferometer setup with the specified directions taken into account.

Answer 2

Step-by-step explanation:

In interferometer , when the movable mirror is moved away by distance d , there is fringe shift on the screen . If n be number of fringes shifted

2 d = n λ

where λ is wavelength of light

Applying this theory for first case when no of fringes shifted is 146

2 d₁ = 146 x 656.3 nm

d₁ = 47909.9 x 10⁻⁹ m

= .048 x 10⁻³ m

= .048 mm

For second case n = 122

2d₂ = 122 x 434 x 10⁻⁹

d₂ = 26474 x 10⁻⁹ m

= .026 mm

So in the second case , mirror must have been moved towards the beam splitter by .048 - .026 = .022 mm

So movement = - 0 .022 mm ( negative displacement )