A double slit interference experiment is set up in a laboratory using a source of blue monochromatic light of wavelength 475nm.the separation of the two slit is 0.40mm and the distance from the slit to the screen where the fringe are observed is 2.20m. calculate the fringe separation, and the angle between the middle of the fringe and the middle of the second bright fringe
Fringe separation = Wavelength x Distance/Slit Separation
Fringe separation = 475nm x 2.2m/0.4mm
Fringe separation = 5.4375mm
Angle between the middle of the fringe and the middle of the second bright fringe = Fringe separation/Distance
Angle between the middle of the fringe and the middle of the second bright fringe = 5.4375mm/2.2m
Angle between the middle of the fringe and the middle of the second bright fringe = 0.2475 radians
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To calculate the fringe separation, we can use the formula:
δy = λL / d
where δy is the fringe separation, λ is the wavelength of light, L is the distance from the slit to the screen, and d is the separation of the two slits.
Plugging in the values, we have:
δy = (475 × 10^-9 m) × (2.20 m) / (0.40 × 10^-3 m)
Simplifying the equation, we get:
δy = 2.60 × 10^-3 m
So, the fringe separation is approximately 2.60 mm.
Now let's move on to the angle between the middle of the fringe and the middle of the second bright fringe. We can use the formula:
θ = λ / d
where θ is the angle, λ is the wavelength of light, and d is the separation of the two slits.
Plugging in the values, we have:
θ = (475 × 10^-9 m) / (0.40 × 10^-3 m)
Simplifying the equation, we get:
θ = 1.19 radians
Converting radians to degrees, we have:
θ ≈ 68.145°
So, the angle between the middle of the fringe and the middle of the second bright fringe is approximately 68.145°.
Hope that brightened up your day with a little bit of scientific humor!
To calculate the fringe separation, we can use the formula:
Fringe separation (d) = (wavelength * distance) / slit separation
Plugging in the given values:
wavelength = 475 nm = 475 × 10^-9 m
slit separation = 0.4 mm = 0.4 × 10^-3 m
distance = 2.2 m
Fringe separation (d) = (475 × 10^-9 m * 2.2 m) / (0.4 × 10^-3 m)
Simplifying the expression:
d = 475 * 2.2 / 0.4 = 2612.5 nm
Therefore, the fringe separation is 2612.5 nm.
To calculate the angle between the middle of the fringe and the middle of the second bright fringe, we can use the formula:
Angle = (wavelength / fringe separation) * (1/2)
Plugging in the given values:
wavelength = 475 nm = 475 × 10^-9 m
fringe separation = 2612.5 nm = 2612.5 × 10^-9 m
Angle = (475 × 10^-9 m / 2612.5 × 10^-9 m) * (1/2)
Simplifying the expression:
Angle = 475 / 2612.5 * (1/2) = 0.0909 radians
Therefore, the angle between the middle of the fringe and the middle of the second bright fringe is approximately 0.0909 radians.
To calculate the fringe separation in a double slit interference experiment, we can use the formula:
Fringe separation (d) = (wavelength * distance to screen) / slit separation
Given the values:
Wavelength (λ) = 475 nm = 475 x 10⁻⁹ m
Slit separation (s) = 0.40 mm = 0.40 x 10⁻³ m
Distance to screen (D) = 2.20 m
Let's plug these values into the formula:
d = (λ * D) / s
= (475 x 10⁻⁹ m * 2.20 m) / (0.40 x 10⁻³ m)
Simplifying the expression:
d = (1.045 x 10⁻⁶ m) / (0.40 x 10⁻³ m)
= 2.613 x 10⁻⁴ m
Therefore, the fringe separation is approximately 2.613 x 10⁻⁴ meters.
Now, to find the angle between the middle of the fringe and the middle of the second bright fringe, we can use the small angle approximation, where the angle (θ) can be calculated using the formula:
θ = fringe separation / distance to screen
Substituting the values we have:
θ = 2.613 x 10⁻⁴ m / 2.20 m
≈ 1.187 x 10⁻⁴ radians
To convert this to degrees, we multiply by (180/π):
θ ≈ 1.187 x 10⁻⁴ radians * (180/π) ≈ 0.0068 degrees
Therefore, the angle between the middle of the fringe and the middle of the second bright fringe is approximately 0.0068 degrees.