Respuesta :
Answer:
The distance between the two slits is 40.11 μm.
Explanation:
Given that,
Frequency [tex]f= 6.37\times10^{14}\ Hz[/tex]
Distance of the screen l = 88.0 cm
Position of the third order y =3.10 cm
We need to calculate the wavelength
Using formula of wavelength
[tex]\lambda=\dfrac{c}{f}[/tex]
where, c = speed of light
f = frequency
Put the value into the formula
[tex]\lambda=\dfrac{3\times10^{8}}{6.37\times10^{14}}[/tex]
[tex]\lambda=471\ nm[/tex]
We need to calculate the distance between the two slits
[tex]m\times \lambda=d\sin\theta[/tex]
[tex]d =\dfrac{m\times\lambda}{\sin\theta}[/tex]
Where, m = number of fringe
d = distance between the two slits
Here, [tex]\sin\theta =\dfrac{y}{l}[/tex]
Put the value into the formula
[tex]d=\dfrac{3\times471\times10^{-9}\times88.0\times10^{-2}}{3.10\times10^{-2}}[/tex]
[tex]d=40.11\times10^{-6}\ m[/tex]
[tex]d = 40.11\ \mu m[/tex]
Hence, The distance between the two slits is 40.11 μm.
