one person drops a ball from the top of the building while another person at the top observers it's motion. will this two people
1 answer:
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Answer:
The smallest film thickness is 117 nm.
Explanation:
Light interference on thin films can be constructive or destructive. Constructive interference is dependent on the film thickness and the refractive index of the medium.
For the first interference (surface nearest to viewer), the minimum thickness can be expressed as:
where n is the refractive index of the bubble film.
Therefore,
∴
To minimize the material usage we have to have the volume requested with the minimum surface area.
The volume is:
And the surface is:
From the first equation we get:
I will use k instead of a number just for the conveince.
We plug this into the second equation and we get:
To find the minimum of this function we have to find the zeros of its first derivative.
Sx will denote the first derivative with respect to x and Sy will denote the first derivative with respect to Sy.
Now let both derivatives go to zero and solve the system (this will give us the so-called critical points).
Now we plug in the first equation into the other and we get:
Now we can calculate y:
And finaly we calculate z:
And finaly let's check our result:
The volume is:
And the surface is:
From the first equation we get:
I will use k instead of a number just for the conveince.
We plug this into the second equation and we get:
To find the minimum of this function we have to find the zeros of its first derivative.
Sx will denote the first derivative with respect to x and Sy will denote the first derivative with respect to Sy.
Now let both derivatives go to zero and solve the system (this will give us the so-called critical points).
Now we plug in the first equation into the other and we get:
Now we can calculate y:
And finaly we calculate z:
And finaly let's check our result: