- #1
quanticism
- 29
- 3
Problem
A thin film of oil (n = 1.30) is located on a smooth, wet pavement. When viewed perpendicular to the pavement, the film reflects most strongly red light at 640 nm and reflects no light at 548 nm. How thick is the oil film?
Equations and Attempt
Refractive index:
air - 1
oil - 1.3
water - 1.33
Assumption: pavement doesn't reflect any light.
Light will undergo a 180 degree phase reversal at the air-oil and oil-water boundaries so the net phase difference in the reflected light is 0.
Thus, for constructive interference, path difference must be an integer number of wavelengths so:
2t = m (640 nm)/1.3, where m is an integer
Similarly, for destructive interference, path difference must be a 1/2 number of wavelength so:
2t = p (548nm)/(2*1.3), where p is an integer
So, I tried to find integers values for m and p for which I could get destructive and constructive interference simultaneously by finding the ratio of m and p:
m/p = 137/320
So minimum integer values for which that ratio is satisfied is m = 137 and p = 320
Subbing it back into the above for t, I obtain t = 33723nm...
A friend told me the answer should be in the domain of the visible spectrum ~(380nm-750nm). But I don't see where I made the mistake. Could someone please nudge me in the right direction?
Note: Alternately, for destructive interference, I could have said:
2t = [(m+1/2)](548nm)/1.3 = (2m+1)(548nm)/[2(1.3)] where m is the "same" integer/order as the one I used for constructive interference.
If I equate this to the eqn for constructive interference, I obtain m = 2.978. Using this, I'll get t = 733.04 nm. However, for this method to work, doesn't m need to be an integer? I guess 2.978 is close to 3 but wouldn't what I did above be more "valid"? (Assuming I didn't make some mistake)
A thin film of oil (n = 1.30) is located on a smooth, wet pavement. When viewed perpendicular to the pavement, the film reflects most strongly red light at 640 nm and reflects no light at 548 nm. How thick is the oil film?
Equations and Attempt
Refractive index:
air - 1
oil - 1.3
water - 1.33
Assumption: pavement doesn't reflect any light.
Light will undergo a 180 degree phase reversal at the air-oil and oil-water boundaries so the net phase difference in the reflected light is 0.
Thus, for constructive interference, path difference must be an integer number of wavelengths so:
2t = m (640 nm)/1.3, where m is an integer
Similarly, for destructive interference, path difference must be a 1/2 number of wavelength so:
2t = p (548nm)/(2*1.3), where p is an integer
So, I tried to find integers values for m and p for which I could get destructive and constructive interference simultaneously by finding the ratio of m and p:
m/p = 137/320
So minimum integer values for which that ratio is satisfied is m = 137 and p = 320
Subbing it back into the above for t, I obtain t = 33723nm...
A friend told me the answer should be in the domain of the visible spectrum ~(380nm-750nm). But I don't see where I made the mistake. Could someone please nudge me in the right direction?
Note: Alternately, for destructive interference, I could have said:
2t = [(m+1/2)](548nm)/1.3 = (2m+1)(548nm)/[2(1.3)] where m is the "same" integer/order as the one I used for constructive interference.
If I equate this to the eqn for constructive interference, I obtain m = 2.978. Using this, I'll get t = 733.04 nm. However, for this method to work, doesn't m need to be an integer? I guess 2.978 is close to 3 but wouldn't what I did above be more "valid"? (Assuming I didn't make some mistake)