Respuesta :
Answer:
[tex] t = \frac{10n}{f}= \frac{10*1.5}{f}= \frac{15}{f}[/tex]
Explanation:
For this case we know that the light without any obstruction and in the free space travels with a speed of [tex] c = 3x10^8 \frac{m}{s}[/tex]
When we have a surface like a glass we know that the velocity is given by the following expression:
[tex] v = \frac{c}{n}[/tex]
Where n is the refraction index, and on this case is given n = 1.5
For this case we know that the lenght of the glass is L and the wavalength is also given [tex] \lambda = \frac{L}{10}[/tex]
We know the following relation between distance and time:
[tex] D = Vt[/tex]
And if we solve for t we got:
[tex] t= \frac{D}{v}[/tex]
For this case the value of D = L and v =c/n and if we replace we got:
[tex] t = \frac{D}{v}= \frac{L}{\frac{c}{n}}= \frac{nL}{c}[/tex] (1)
Now we need to found a way to incorporate the wavelength into this formula and we have the following expression:
[tex] c = \lambda f[/tex]
If we replace this condition into equation (1) we got:
[tex] t = \frac{nL}{\lambda f}[/tex]
And we can use the condition that [tex] \lambda = \frac{L}{10}[/tex] and we have this:
[tex] t = \frac{nL}{\frac{L}{10} f}[/tex]
We can cancel the L terms and we have just:
[tex] t = \frac{10n}{f}= \frac{10*1.5}{f}= \frac{15}{f}[/tex]
And that would be the time that it takes a short pulse of light to travel from one end of the glass to the other.
It will take "[tex]t = \frac{15}{f}[/tex]". A further explanation is below.
Given:
Index of refraction,
- n = 15
Wavelength,
- λ = [tex]\frac{L}{10}[/tex]
As we know,
→ [tex]t = \frac{d}{v}[/tex]
[tex]t = \frac{L}{\frac{c}{n} } = n\times \frac{L}{c}[/tex]
here, [tex]c = \lambda\times f[/tex]
then,
→ [tex]t = n\times \frac{L}{c} = n\times \frac{L}{\lambda\times f}[/tex]
By substituting the values, we get
[tex]= n\times \frac{L}{\lambda\times f}[/tex]
[tex]= 10\times \frac{n}{f}[/tex]
[tex]t = \frac{15}{f}[/tex]
Thus the above answer is correct.
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