The lab experiment is repeated again with the same two glass plates and the same sodium lamp but with a different human hair. The space between the plates is filled with a transparent silicon grease that has n = 1.52. The glass plates each have refractive index 1.20. The separation between adjacent dark fringes is measured to be 0.750 mm. Calculate the diameter of the hair. (The wavelength emitted by the lamp is 589.3 nm. The length of the plates is 12.0 cm.)

Question

Mathematics

Jorden

2 October, 15:30

The lab experiment is repeated again with the same two glass plates and the same sodium lamp but with a different human hair. The space between the plates is filled with a transparent silicon grease that has n = 1.52. The glass plates each have refractive index 1.20. The separation between adjacent dark fringes is measured to be 0.750 mm. Calculate the diameter of the hair. (The wavelength emitted by the lamp is 589.3 nm. The length of the plates is 12.0 cm.)

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Irvin Crosby · Answer 1

diamerer of the hair (t) 3.11 X 10^{-5} m

Step-by-step explanation:

The first dark spot is at the zero location where the glass plates touch. To find the number of dark fringes after first dark fringe, divide 12 cm by 0.75 mm (.075 cm)

12/.075 = 160.0

total number of additional bright fringe is 156 because there is no further portion for extra dark fringe.

diamerer of the hair (t) can be derived as

2nt = (m +.5) * wavelength

2 (1.52) (t) = (160.5) (589.3 X 10^{-9})

t = 3.11 X 10^{-5} m