A double-slit experiment uses coherent light of wavelength 633 nm with a slit separation of 0.100 mm and a screen
placed 2.0 m away.
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To understand the double-slit experiment and find the answer to your question, we will need to apply some principles of optics and the wave nature of light.
The double-slit experiment involves shining light through two slits and observing the resulting interference pattern on a screen placed some distance away. This experiment is used to study the wave-like nature of light.
Based on the given information, we have a coherent light source with a wavelength of 633 nm and a slit separation of 0.100 mm. We need to find the pattern produced on the screen placed 2.0 m away.
1. Determine the distance between the slits:
The slit separation is given as 0.100 mm. Convert this to meters by dividing by 1000:
Slit separation = 0.100 mm ÷ 1000 = 0.0001 m
2. Calculate the angle between the central maximum and the first-order maximum:
The angle can be calculated using the formula:
d sinθ = mλ
where d is the slit separation, θ is the angle, m is the order of the maximum (in this case, 1), and λ is the wavelength of light.
Rearranging the formula, we get:
sinθ = (mλ) / d
Substitute the values:
sinθ = (1 * 633 nm) / 0.0001 m
Convert the wavelength to meters by dividing by 10^9:
sinθ = (1 * 633 nm) / (0.0001 m * 10^9)
Calculate the value of sinθ:
sinθ = 6.33 * 10^-7
3. Calculate the angle itself:
To find the angle θ, we need to take the inverse sine (sin⁻¹) of the value we obtained:
θ = sin⁻¹(6.33 * 10^-7)
Use a scientific calculator to find the inverse sine of the value.
4. Calculate the distance between adjacent maxima:
For small angles, we can use the approximation:
y ≈ mλL / d
where y is the distance between adjacent maxima, m is the order of the maximum, L is the distance between the screen and the slits, d is the slit separation, and λ is the wavelength of light.
Substitute the values:
y = (1 * 633 nm * 2.0 m) / 0.0001 m
Convert the wavelength to meters by dividing by 10^9:
y = (1 * 633 nm * 2.0 m) / (0.0001 m * 10^9)
Calculate the value of y:
y = 1.266 * 10^-4 m
So, based on the given information, the distance between adjacent maxima on the screen is approximately 1.266 * 10^-4 meters.