Quick help with math in thin film problem

In summary, the conversation discusses the equation (2*m2 + 1) / (2*m1) =λ1 / λ2 = 640 nm / 512 nm = 1.25 and the attempt to solve for m1 and m2. It is discovered that using m1=m2=2 satisfies the equation, but there is uncertainty on how to reach this conclusion mathematically. Ultimately, the solution is found to be m2 = 1.25m1 - 0.5.
  • #1
Anuj68
1
0

Homework Statement


(1 / 2) (λ1 /nfilm) (m1) = (1 /4) (λ2 / nfilm) (2m2 +1)

(2*m2 + 1) / (2*m1) =λ1 / λ2 = 640 nm / 512 nm = 1.25

We want to solve for m1 and m2.
I have realized that using m1=m2=2 works but I can't figure out how to reach this conclusion mathematically.

Please, any help will be greatly appreciated.


Homework Equations





The Attempt at a Solution

 
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  • #2
Welcome to PF!

Hi Anuj68! Welcome to PF! :smile:

(try using the X2 icon just above the Reply box :wink:)
Anuj68 said:
(2*m2 + 1) / (2*m1) =λ1 / λ2 = 640 nm / 512 nm = 1.25

We want to solve for m1 and m2.
I have realized that using m1=m2=2 works but I can't figure out how to reach this conclusion mathematically.

(2m2 + 1)/(2m1) = 1.25

ie (m2 + 0.5)/(m1) = 1.25.

so m2 = 1.25m1 - 0.5 :wink:
 

1. How can I quickly solve a math problem related to thin film?

There are a few steps you can follow to quickly solve a math problem in thin film. First, make sure you understand the problem and what is being asked. Then, identify the relevant equations and variables. Next, plug in the given values and solve for the unknown variable. Finally, double check your answer and make sure it makes sense in the context of the problem.

2. What are the most common equations used in thin film problems?

The most common equations used in thin film problems are the Fresnel equations, Snell's law, and the thin film interference equation. These equations help calculate properties such as reflectance, transmittance, and phase shift in thin film systems.

3. How do I know which equation to use for a specific thin film problem?

The equation you should use for a specific thin film problem depends on what information is given and what information is being asked for. Make sure you understand the problem and what is being asked, and then identify the relevant equations that can help you solve for the unknown variable.

4. What are some common mistakes to avoid when solving thin film math problems?

Some common mistakes to avoid when solving thin film math problems include using the wrong equation, plugging in the wrong values, and performing incorrect calculations. It is also important to pay attention to units and make sure they are consistent throughout the problem.

5. How can I check my answer for a thin film math problem?

To check your answer for a thin film math problem, you can plug your calculated values back into the original equation and make sure they satisfy the given conditions. You can also compare your answer to the expected range or value, if provided. Additionally, it is helpful to double check your calculations and make sure you did not make any mistakes along the way.

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