Light of a single frequency is incident on a pair of narrow slits that are a distance of 0.10 mmapart. A series of bright and dark fringes is observed on a screen a distance of 2.0 m away. Thedistance between adjacent bright fringes is 8.0 mm.lightscreensecond-order dark fringeslitszero-order bright fringedistance betweenbright fringes = 8.0 mm2.0 mNOT TO SCALEWhat is the path difference of the light waves from the two slits that meet at the second-orderdark fringe?A 2.0 10 –7 mB 4.0 10 –7 mC 6.0 10 –7 mD 8.0 10 –7 m
Question
Light of a single frequency is incident on a pair of narrow slits that are a distance of 0.10 mmapart. A series of bright and dark fringes is observed on a screen a distance of 2.0 m away. Thedistance between adjacent bright fringes is 8.0 mm.lightscreensecond-order dark fringeslitszero-order bright fringedistance betweenbright fringes = 8.0 mm2.0 mNOT TO SCALEWhat is the path difference of the light waves from the two slits that meet at the second-orderdark fringe?A 2.0 10 –7 mB 4.0 10 –7 mC 6.0 10 –7 mD 8.0 10 –7 m
Solution
To solve this problem, we need to understand the concept of interference and diffraction of light.
In a double-slit experiment, a dark fringe is formed when the path difference between the two slits is an odd multiple of half the wavelength (λ/2). This is because the waves from the two slits are out of phase and destructively interfere at these points.
The path difference (d) can be calculated using the formula:
d = m * λ
where m is the order of the fringe. For a dark fringe, m is an odd number, so for the second-order dark fringe, m = 3 (as it's the third dark fringe, the first being the zero-order bright fringe).
So, the path difference for the second-order dark fringe is:
d = 3 * λ
However, we don't know the wavelength of the light. But we can calculate it using the formula for the distance between bright fringes (y) on the screen:
y = L * λ / d
where L is the distance from the slits to the screen, and d is the distance between the slits. Rearranging for λ gives:
λ = y * d / L
Substituting the given values:
λ = 8.0 * 10^-3 m * 0.10 * 10^-3 m / 2.0 m = 4.0 * 10^-7 m
Substituting λ back into the formula for the path difference gives:
d = 3 * λ = 3 * 4.0 * 10^-7 m = 1.2 * 10^-6 m
However, none of the given options match this result. There may be a mistake in the problem or the options.
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