Interference of Light waves HELP

[yoshima]

I've been trying to get the anwser to this question for awhile. Any help is appreciated.

1. A glass plate (n=1.61) is covered with a thin, uniform layer of oil (n=1.24). A light beam of variable wavelength from air is incident normally on the oil surface. Observation of the reflected beam shows destructive interference at 549 nm and constructive interference at 727 nm. From this information, calculate the thickness of the oil film.

thanks

 

[Doc Al]

find the phase difference

Show what you've tried and where you are stuck.

Here's a hint to get you started: Light will reflect off the surface of the oil and the surface of the glass. These two reflections will interfere. What phase difference must they have to interfere constructively? destructively? How does the phase difference depend on the thickness of the oil?

 

[yoshima]

the solution that i though would be right

they way I've bee doing it is by using the formula for both destructive and constructive interference.

Constructive inter. --> 2nt=m*(lambda)c
destructive inter. --> 2nt=(m+1/2)*(lambda)d

Because the thickness of the film is the same --> 2nt = 2nt

:. (m+1/2)/(m) = (lambda)c/(lambda)d = 727/549

and from here solve for mc and sub that into the constructive formula 2nt=m*(lambda)c and you get the thickness.. but teh anwser is not right.

Is there another way of solving this problem or am i solving the wrong way.

 

[Doc Al]

Constructive inter. --> 2nt=m*(lambda)c
destructive inter. --> 2nt=(m+1/2)*(lambda)d

In your second equation, what you have as "m + 1/2" could also be m + 3/2, m + 5/2, etc. You need to find the value that makes m an integer. Trial and error!