A double-slit diffraction pattern is formed on a distant screen. If the separation between the slits decreases, what happens to the distance between interference fringes? Assume the angles involved remain small.
A double-slit diffraction pattern is formed on a distant screen. If the separation between the slits decreases, what happens to the distance between interference fringes? Assume the angles involved remain small.
The distance between interference fringes increases.
The distance between interference fringes remains the same.
The effect cannot be determined unless the distance between the slits and the screen is known.
The distance between interference fringes also decreases.
The first off center maximum occurs when the path lengths to the screen from the two slits differs by one wavelength. If you move the slits closer together, the angle to the screen must increase to get path lengths a wavelength different.
Therefore is you decrease the spacing between slits, you WIDEN the interference pattern of the target.
At a fixed angle from the slits, if you decrease the distance between the slits the path length difference decreases. So, the angle needs to increase to get back to the same path length difference (half the wavelenght for a fringe).
I had that the distance between interference fringes also decrease but I go it wrong
this is the
d sin(theta) = m (lambda)
I am confused on what its asking now,
isn't is d?
yes
For the same m (lambda)
for smaller d, you need BIGGER theta
so the peaks on the target will be further apart as d shrinks.
To understand what happens to the distance between interference fringes when the separation between the slits decreases in a double-slit diffraction pattern, we can use the basic principles of wave interference.
When light passes through the slits, it diffracts and forms a pattern of alternating light and dark bands on a screen, known as interference fringes. These fringes occur due to the constructive and destructive interference of the light waves from the two slits.
The distance between interference fringes, known as the fringe separation or fringe spacing, can be determined by the following equation:
λ * L / d = X
Where:
λ is the wavelength of the light source,
L is the distance from the double slit to the screen,
d is the separation between the slits,
and X is the distance between adjacent interference fringes.
Assuming the angles involved (related to the screen and the slits) remain small, we can observe some key features:
1. From the equation, the fringe separation is inversely proportional to the separation between the slits (d).
2. As the separation between the slits decreases, the fringe separation (X) will increase.
Therefore, when the separation between the slits decreases, the distance between interference fringes increases.
Hence, the correct answer is: "The distance between interference fringes increases."