Physics, 30.11.2019 00:31 bigmandavis

When monochromatic light shines perpendicularly on a soap film (n = 1.33) with air on each side, the second smallest nonzero film thickness for which destructive interference of reflected light is observed is 443 nm. what is the vacuum wavelength of the light in nm?

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Answer from: symonya

To develop this problem it is necessary to apply the concepts related to destructive interaction.

By definition we know that it is given as

$\Delta l = (m+\frac{1}{2})\lambda$

Where,

l = Distance between slits

m = Any integer representing the number of repetition of spectrum

$\lambda = Wavelength$

There is a change in phase at the upper side of the film which causes the phase shift since the index of refraction of the soap film is greater than that of air.

The extra traveled distance is twice the film thickness since the light shines perpendicularly and the wave travels back and fourth through the film, so

$2t +\frac{1}{2} \lambda = (m+\frac{1}{2})\lambda$

$2t = m\lambda$

At m= 2 (second smalles nonzero thickness) we have that

$2t = 2\lambda$

$t = \lambda$

The index of refraction of soap is given so the relationship is

$\lambda = \frac{\lambda{vacuum}}{n}$

Substituting the previos equation

$t = \frac{\lambda_{vacuum}}{n}$

Re, arrange to find \lambda_{vacuum}

$\lambda_{vacuum} = tn$

$\lambda_{vacuum} = 443*1.33$

$\lambda_{vacuum} = 575.89nm$

Therefore the vacuum wavelength of the light is 575.89nm

Answer from: Quest

answer: at 24 february, 2014 the population gets twice of its initial population.

explanation:

since we have given that

the population for alpha city, t years after january 1, 2004 is given as

$p(t)=0.3t^2+6t+80$

first we find out the initial population, i.e. t=0,

so, our quadratic equation becomes,

$p(0)=0+0+80=80$

according to question, we have said that if the population has twice its initial population, then it becomes

$p(t)=2\times 80=160$

so, time taken to reach this above mentioned population is given by

$160=0.3t^2+6t+80\\\\160-80=0.3t^2+6t\\\\80=0.3t^2+6t\\\\0.3t^2+6t-80=0\\\\\text{using quadratic formula ,we get }\\\\t_{1,\: 2}=\frac{-60\pm \sqrt{60^2-4\cdot \: 3\cdot \: 800}}{2\cdot \: 3}\\\\t=-29.14\ and\ t=9.149$

now, we know that time can't be negative so, we take t=9.149 years.

hence, at 24 february, 2014 the population gets twice of its initial population.

Answer from: Quest

the box does not move because you need to use a force greater than 300 n. you are only using 50 n. it needs to at least be 301 n for the box to move because then it is an unbalanced force and it will move the way that the greater force is pushing it. if you use only 300 n it will be a balanced force and will not move because the force you are exerting on the box is the same as its force.

hope this !

im sorry if i went too in depth, i am going to include a link to a video on khan academy that will explain this. hope that you like the video and that it explains more in detail to you.

that is the link.

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When monochromatic light shines perpendicularly on a soap film (n = 1.33) with air on each side, the...

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