HW help (Double Slit, Resolving power etc)

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(a) A double-slit experiment is set up using red light (l = 708 nm). A first order bright fringe is seen at a given location on a screen. What wavelength of visible light (between 380 nm and 750 nm) would produce a dark fringe at the identical location on the screen?
l = nm

All right so i know
d * sin theta = m * wavelength

How do i find the Distance and the angle?

 

[Max Eilerson]

The condition for constructive interference is what you have written down (i.e. peak on peak), but destructive interference happens when you have a trough meet a peak, i.e. there is a half wavelength difference so for destructive interference (dark fringe) dsin (\theta) = (m + 0.5)\lambda. You should be able to go from there.

 

[Alt+F4]

(b) A new experiment is created with the screen at a distance of 1.8 m from the slits (with spacing 0.08 mm). What is the distance between the second order bright fringe of light with l = 691 nm and the third order bright fringe of light with l = 414 nm? (Give the absolute value of the smallest possible distance between these two fringes: the distance between bright fringes on the same side of the central bright fringe.)







Ok so
D sin theta = m * wavelength

Distance is 2.2?
I am going to find theta
m = 1
wavelength is 698 in one part, and then i do the quation again for 413 right?

 

[OlderDan]

(b) A new experiment is created with the screen at a distance of 1.8 m from the slits (with spacing 0.08 mm). What is the distance between the second order bright fringe of light with l = 691 nm and the third order bright fringe of light with l = 414 nm? (Give the absolute value of the smallest possible distance between these two fringes: the distance between bright fringes on the same side of the central bright fringe.)







Ok so
D sin theta = m * wavelength

Distance is 2.2?
I am going to find theta
m = 1
wavelength is 698 in one part, and then i do the quation again for 413 right?

Don't lose track of the statement about the different orders of the finges. What is m for second order, and for third order?

 

[Alt+F4]

Don't lose track of the statement about the different orders of the finges. What is m for second order, and for third order?

2 for second order, and 3 for third order

 

[Alt+F4]

got the answer, thanks

 

[Max Eilerson]

You don't actually need to find the distance at all. You will have two equations equal to dsin (\theta), and you just have to solve for the 1 unknown (wavelength).

 

[Max Eilerson]

got the answer, thanks

and that would be?

 

[Alt+F4]

.00315 m
...

 

[Max Eilerson]

Yes that's correct for (b). What answer did you get for (a).