A laser emitting light with a wavelength of 560 nm is directed at a single slit, producing an interference pattern on a screen that is 3.0 m away. The central maximum is 5.0 cm wide.
Determine the width of the slit and the distance between adjacent maxima.
To find the width of the slit, we can use the formula for the width of the central maximum in a single slit diffraction pattern:
sin(θ) = (λ / a)
Where θ is the angle from the central maximum, λ is the wavelength of light, and a is the width of the slit.
Since the central maximum is 5.0 cm wide, we can convert it to meters:
5.0 cm = 0.05 m
We are given that the wavelength of light is 560 nm, so we can convert it to meters as well:
560 nm = 560 × 10^(-9) m
Now we can rearrange the formula and solve for the width of the slit:
a = λ / sin(θ)
a = (560 × 10^(-9) m) / sin(θ)
The distance between adjacent maxima is given by the formula:
y = (λ × L) / a
Where y is the distance between adjacent maxima, λ is the wavelength of light, L is the distance from the slit to the screen, and a is the width of the slit.
We are given that the distance from the slit to the screen is 3.0 m:
L = 3.0 m
Substituting the values into the formula, we have:
y = (560 × 10^(-9) m × 3.0 m) / (560 × 10^(-9) m)
Simplifying, we get:
y = 3.0 m
Therefore, the width of the slit is 560 × 10^(-9) m and the distance between adjacent maxima is 3.0 m.
What would the effect on this pattern be, if
If the width of the slit is decreased, the central maximum would become wider and the intensity of the other maxima would increase. This is because a narrower slit allows for less diffraction, resulting in a broader central maximum. Additionally, the narrower slit would cause more interference between the diffracted waves, leading to increased intensity at the adjacent maxima.
On the other hand, if the width of the slit is increased, the central maximum would become narrower and the intensity of the other maxima would decrease. This is because a wider slit allows for more diffraction, resulting in a narrower central maximum. Additionally, the wider slit would cause less interference between the diffracted waves, leading to decreased intensity at the adjacent maxima.
What would the effect on this pattern be, if the width of the slit was smaller?
If the width of the slit is smaller, the central maximum would become wider and the intensity of the other maxima would increase. This is because a smaller slit allows for less diffraction, resulting in a broader central maximum. Additionally, the smaller slit would cause more interference between the diffracted waves, leading to increased intensity at the adjacent maxima.
In other words, decreasing the width of the slit would result in a broader diffraction pattern with more pronounced intensity at the adjacent maxima.
What would the effect on this pattern be, if the screen was moved further away?
If the screen is moved further away, the diffraction pattern would spread out and the distance between adjacent maxima would increase. This occurs because the angle of diffraction becomes smaller as the distance between the slit and the screen increases, resulting in a wider spacing between the interference fringes.
Mathematically, the distance between adjacent maxima in a single slit diffraction pattern is given by the formula:
y = (λ * L) / a
Where y is the distance between adjacent maxima, λ is the wavelength of light, L is the distance from the slit to the screen, and a is the width of the slit. As L increases, the distance between adjacent maxima (y) also increases.
Therefore, if the screen is moved further away, the diffraction pattern would become more spread out, with wider spacing between adjacent maxima.
What would the effect on this pattern be, if a larger wavelength of light was used?
If a larger wavelength of light is used, the diffraction pattern would become more spread out and the distance between adjacent maxima would increase. This occurs because the wavelength of light is directly proportional to the distance between adjacent maxima in a single slit diffraction pattern.
Mathematically, the distance between adjacent maxima in a single slit diffraction pattern is given by the formula:
y = (λ * L) / a
Where y is the distance between adjacent maxima, λ is the wavelength of light, L is the distance from the slit to the screen, and a is the width of the slit. As the wavelength (λ) increases, the distance between adjacent maxima (y) also increases.
Therefore, if a larger wavelength of light is used, the diffraction pattern would become more spread out, with wider spacing between adjacent maxima.