Question

Light of wavelength 610 nm falls on a slit that is 3.90×10⁻³ mm wide. How far the first bright diffraction fringe is from the strong central maximum if the screen is 10.5 maway. Express your answer to three significant figures and include the appropriate units.

Answer 1

To find the position of the first bright diffraction fringe from the central maximum in a single-slit diffraction scenario, we use the minima condition equation and then find the position using the small-angle approximation for the tangent function.

Step-by-step explanation:

The question involves calculating the position of the first bright diffraction fringe using the principles of single-slit diffraction. To find how far the first bright diffraction fringe is from the central maximum, we can use the formula for single-slit diffraction:

L \(\theta\) = (m + \(\frac{1}{2}\)) \(\lambda\)

where L is the distance from the slit to the screen, \(\theta\) is the diffraction angle, m is the fringe order (m = 0 for the first bright fringe outside the central maximum), and \(\lambda\) is the wavelength of the light.

The width of the slit is given as 3.90\(\times\)10^-3 mm, or 3.90\(\times\)10^-6 meters, the wavelength \(\lambda\) is given as 610 nm or 610\(\times\)10^-9 meters, and the screen distance L is 10.5 meters. We first find the angle \(\theta\) using the equation for the condition for minima in single-slit diffraction:

sin(\(\theta\)) = (m + \(\frac{1}{2}\))\(\frac{\lambda\}{d}\)

Then, we use the angle \(\theta\) to find the position of the first bright fringe from the central maximum (y = L\(\tan(\theta\))). Since for small angles \(\tan(\theta\) \approx \sin(\theta\)), we can simplify this to y = L\(\sin(\theta\)):

y = 10.5 \times \(\sin(\theta\))

After calculating \(\theta\) and subsequently y, we get the position of the first bright fringe.