23. Two slits are separated by 0.180 mm. An interference pattern is formed on a screen 80.0 cm away by 656.3-nm light.
Calculate the fraction of the maximum intensity a distance y 5 0.600 cm away from the central maximum.

The fraction of the maximum intensity a distance y 5 0.600 cm away from the central maximum is 0.97.

Explanation:

d = 0.180 mm = 1.8 x 10⁻⁴ m

L = 80 cm = 0.8 m

λ = 656.3 nm = 6.563 x 10⁻⁷ m

y = 0.6 cm = 6 x 10⁻³ m

we know that the equation of the intensity for two slits interference equation is

I = cos²(πdy/λL)

where

I = intensity

 = maximum intensity

d = distance of two slits

y = the distance of the interference with the central

L = the distance of screen and the slits

λ = wavelength

so,

I = cos²(πdy/λL)

I/  = cos²(πdy/λL)

          = cos²[π (1.8 x 10⁻⁴) (6 x 10⁻³)/(6.563 x 10⁻⁷) (0.8 )]

          = 0.97

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.

0.93xc=0.93x3x10^8m/s

2.54cm is 1 inch

360seconds i 1 hr