How wide is the central diffraction peak on a screen 2.40 m behind a 0.0368-mm-wide slit illuminated by 578-nm light? Express your answer using three significant figures.

The width of the central diffraction peak is 0.0754 m.

Explanation:

Given:

Distance of screen from slit (L) = 2.40 m

Width of the slit (a) = 0.0368 mm = 0.0368 × 10⁻³ m

Wavelength of light (λ) = 578 nm = 578 × 10⁻⁹ m

Now, we know that, the location of the first diffraction minimum from the center is given as:

Now, in order to find the width of the central diffraction peak we need to consider the distance 'y' both above and below the central line.

Therefore, the width of the central diffraction peak is given as twice the distance 'y'.

So, Width of central diffraction peak is,

Now, plug in the values given and solve for width 'W'. This gives,

Therefore, the width of the central diffraction peak is 0.0754 m.

russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

where is unknown. because the position is parabolic, there is symmetry about the midpoint at , and we know that

so that the position function is

which means the velocity is

then the total distance traveled is

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at and ends at , so its displacement is 0.