Calculate Radius of Wire in Air Wedge Formed by Glass Plates

[U262241]

An air wedge is formed between two glass plates separated at one edge by a ver fine wire. When the wedge is illumindated from above by 688 nm light, 29 dark fringes are observed. Calculate the radius of the wire. Show answer in micro meters

I have tried many different things with this problem and cannot come up with the correct answer. Here is the last thing I did. Since 39 dark fringes are seen; 39 light fringes will also be seen. Where t=0 will be the first dark fringe. Which means fringe 78 is a light fringe, which is right next to the wire separating the two glass plates. The formula is:

t = [((m - 1/2)*lamda) / 2] * 1e+6 micro m/m

This will give the diameter of t. Divide the diameter by 2 to get the radius. Unfortunately, this does not give the correct answer. What am I doing wrong. The answer I came up with is 13.158 micro meters.

 

[Chi Meson]

Each time the fringes go from dark to light to dark again, by what fraction of a wavelength has the air gap increased?

 

[U262241]

Should it be +1/2 instead of -1/2?

 

[Chi Meson]

No no, forget the freakin' formula for a second. Do you know how these fringes show up? THe two paths of light, one slightly longer, etc? Each time you get to another dark fringe, how much farther has the second ray of light traveled?

 

[samsam89]

i using the formula with : 2t = n (w)

**P/s : w = wavelength , t = thickness

regarding ur ques --> w= 688nm , n (dark) = 29

hence,
t = (29*688nm) / 2
= 9.976 micro meter

Since the ques need ans in radius, therefore
t / 2 = 9.976/2
= 4.988 micro meter ( Ans )Done! Is it correct??

 

[ikram-zidane]

am i correct to say that since for the 1st dark fringe, we consider n=0, thus the value of n should be 28 instead of 29 ?

hence, making it:-

2 (t) = (28) (688*10^-9)

where t = 9.63 micrometer
and the radius is 4.82 micrometer ?