Understanding the Role of 'y' in Interference of Light Waves Equations

[dekoi]

Equations dealing with the interference of light waves have a variable 'delta y'. My biggest problem is understanding what 'y' represents? Does it define the distance between two adjacent fringes? Or the distance of a fringe from the origin? this scepticism might have been the reason for my confusion in these questions.

1.) Two antennas separated by 300m simultaneously broadcast identical signals of = wavelength. a.) A car is traveling north and is at 400m north of the midpoint line between the two signals. What is the wavelength?

My solution:
d=3.00m
L=1000m
n=2
y = 400m (from center/origin).

I solved for wavelength and got an answer of 60m. the correct answer is supposedly 55.7m.

Part 'b' of the question: How much further does the car have to travel to encounter the next minimum in reception? (Do not use small-angle approximation).

I understand i must be solving for the dark fringes now. But the formula is confusing since 1.) i can't use small-angle approximation, and 2.) I am still confused as to what 'y' represents.

2.) Light with wavelength 442nm passes through a double-slit system that has a slit separation of 0.400mm. Determine how far the screen must be placed away from the sources to create two fringes directly across from the slits and one frindge between those.

I have wavelength, distance between slits, and i could potentially find y. I must ultimately solve for L (length between screen and slits). Fistly, i have to find where the two fringes which are directly across the slits really are. I assumed that the top fringe is 'd' away from the bottom fringe. Since there is a nother frindge in betwee, the distance between frindges would be 0.4mm/2. Once again, my problem with 'y' haunts me. Should 'y' be the 0.2mm or something else?

Thank you.

 

[daniel_i_l]

There are two equations with y.
One with y (not delta y) and 'n' which specifies which fringe you're talking about. This gives the distance of the n fringe from the middle at distance L:
y = ((n - 0.5)*wavelength*L)/d
The other one has delta y and no 'n'. This gives the distance between any two adjacent fringes at distance L. We got this equation by using the first one and subtracting the distance of the n+1 fringe from the n fringe giving the distance between them:
delta y = (wavelength*L)/d

Also, if you can't use small angle approximation, then instead of saying that
sin(angle) = (n-0.5)*wavelength/d = y/L and finding L which is really only true for tan(angle), then just find the angle by
sin(angle) = (n-0.5)*wavelength/d, and find L by doing:
tan(angle) = y/L
Hope that helped!

 

[dekoi]

Can anyone verify the above, and also help on the other questions that i posted? Thank you.

 

[dekoi]

Revised Question

Question number 2 was solved.

Regarding Question number1:

I use 300m for d (separation of slits), 1000m for length between "screen" and slits (Sources). Should n = 2? And should y = 400m?

Once again, i calculate 60m. But the correct answer should be 55.7m. Any ideas?
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[dekoi]

?? Anyone? .