(a) What is the path difference ? for the two slits at the location y?

(b) Express this path difference in terms of the wavelength.

nicekikah
2021-03-26
Answered

A pair of slits, separated by 0.150 mm, is illuminated by light having a wavelength of ? = 561 nm. An interference pattern is observed on a screen 122 cm from the slits. Consider a point on the screen located at y = 2.00 cm from the central maximum of this pattern.

(a) What is the path difference ? for the two slits at the location y?

(b) Express this path difference in terms of the wavelength.

(a) What is the path difference ? for the two slits at the location y?

(b) Express this path difference in terms of the wavelength.

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Faiza Fuller

Answered 2021-03-28
Author has **108** answers

our formula for double slit interference is:

$d\mathrm{sin}\left(t\right)=m\left(w\right)$

where d is the width of the slits

where t is the angle from the slits

where m is the corresponding fringe from the central fringe

where w is the wavelength

using trig, we can find$\mathrm{sin}\left(t\right)$ to be:

$\mathrm{sin}\left(t\right)=\frac{y}{L}$

where y is the distance from central fringe to corresponding fringe

where L is the distance from slit to screen

our formula now becomes:

$d\left(\frac{y}{L}\right)=m\left(w\right)$

where both sides represent the path difference:

path difference=d(y/L)

path difference = .150e-3(2e-2/122e-2)

path difference = 2.459e-6 m

In terms of the wavelength:

2.459e-6/561e-9 = 4.4w

where d is the width of the slits

where t is the angle from the slits

where m is the corresponding fringe from the central fringe

where w is the wavelength

using trig, we can find

where y is the distance from central fringe to corresponding fringe

where L is the distance from slit to screen

our formula now becomes:

where both sides represent the path difference:

path difference=d(y/L)

path difference = .150e-3(2e-2/122e-2)

path difference = 2.459e-6 m

In terms of the wavelength:

2.459e-6/561e-9 = 4.4w

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