Distance between m=0/m=1 bright fringes

[crazyog]

Homework Statement

Two slits separated by 2.00x10^-5 are illuminated by light of wavelength 500nm. If the scree is 8.0m from the slits what is the distance between m = 0 and m=1 bright fringes?
answer is 10 cm

Homework Equations

d=m*lambda*L/y (for the short cute..for small angles)

The Attempt at a Solution

at m=0 d=0

at m=1
d=1*(500*10^-9)(8.0 m)/(2.0*10^-5) = 0.2m

so I am getting double...but I can't find a reason t multiply it by 1/2 ...

hmm
please help!

also, do i alway use m for bright fringe and (m+1/2) for dark...?

 

[crazyog]

I figured out there was a mistake on the answer sheet and the answer is 20 cm


haha thanks anyways

 

[baba89]

I would like to clarify a few points about the given problem and the solution provided. Firstly, the distance between the two slits should be stated in meters (m) rather than in nanometers (nm). So, the correct value for the distance between the slits would be 2.00x10^-5 m.

Secondly, the formula used to calculate the distance between bright fringes (d=m*lambda*L/y) is valid only for small angles, as mentioned in the problem. This means that the distance between the screen and the slits (L) should be much larger than the distance between the slits (d). In this case, L is given as 8.0 m and d is 2.00x10^-5 m, which satisfies the condition for small angles.

Now, coming to the solution provided, the distance between m=0 and m=1 bright fringes would be the distance between the central bright fringe (m=0) and the first bright fringe (m=1). This can be calculated using the formula d=m*lambda*L/y. So, at m=0, the distance would be 0, and at m=1, the distance would be 1*(500x10^-9)(8.0)/(2.00x10^-5) = 0.2 m. This means that the distance between m=0 and m=1 bright fringes is 0.2 m.

Finally, the use of m and (m+1/2) for bright and dark fringes depends on the type of interference pattern observed. For the given problem, where two slits are used, the bright fringes occur at integer values of m (m=0,1,2,...) and the dark fringes occur at half-integer values of m (m=1/2,3/2,5/2,...). This is known as the double-slit interference pattern. However, for other types of interference patterns, the use of m and (m+1/2) may vary.

I hope this clarifies any confusion and helps in understanding the solution to the given problem.