Coherent light of frequency 6.30 1014 Hz passes through two thin slits and falls on a screen 75.0 cm away. You observe that the third bright fringe occurs at ±3.06 cm on either side of the central bright fringe.
(a) How far apart are the two slits?
I got --> .035 mm
(b) At what distance from the central bright fringe will the third dark fringe occur?
*Needs to be in cm
To solve this problem, we can use the concept of interference of light waves. In interference, when coherent light passes through two narrow slits, it diffracts and forms a pattern of bright and dark fringes on a screen.
(a) To find the distance between the two slits, we can use the equation:
d * sin(θ) = m * λ
Where:
d = distance between the slits
θ = angle between the central bright fringe and the third bright fringe
m = order of the fringe (in this case m = 3)
λ = wavelength of the light
Given that the frequency of the light is 6.30 * 10^14 Hz, we can find the wavelength using the formula:
λ = c / f
Where:
λ = wavelength
c = speed of light (approximately 3 * 10^8 m/s)
f = frequency
Substituting the values into the equation, we get:
λ = (3 * 10^8 m/s) / (6.30 * 10^14 Hz)
Now, we can substitute the calculated wavelength into the equation for the distance between the slits:
0.0306 m * sin(θ) = 3 * (calculated wavelength)
Solving for θ, we find:
θ = sin^(-1) [(3 * (calculated wavelength)) / 0.0306 m]
Finally, we can calculate the distance between the slits using the equation:
d = (λ * distance to the screen) / sin(θ)
Plugging in the values, we get:
d = [(calculated wavelength) * 0.75 m] / sin(θ)
Solving for d, we find:
d ≈ 0.035 mm
So, the distance between the two slits is approximately 0.035 mm.
(b) To find the distance from the central bright fringe where the third dark fringe occurs, we can use the concept of dark fringes being located midway between adjacent bright fringes. In this case, the distance from the central bright fringe to the third dark fringe will be half the distance between the central and third bright fringes.
Given that the distance from the central bright fringe to the third bright fringe is 3.06 cm, we can find the distance from the central bright fringe to the third dark fringe using the equation:
distance to the third dark fringe = (1/2) * (distance to the third bright fringe)
Plugging in the values, we get:
distance to the third dark fringe = (1/2) * (3.06 cm)
Therefore, the distance from the central bright fringe to the third dark fringe is approximately 1.53 cm.