Answer :
Answer:
The wavelength is [tex]5.57\times10^{-7}\ m[/tex]
The frequency is [tex]5.4\times10^{14}\ Hz[/tex]
Explanation:
Given that,
Distance between slits d= 0.044 mm
Distance between fringe and center of the pattern y= 8.1 cm
Distance between slits and fringes D = 6.40 m
We need to calculate the wavelength
For constructive interference
[tex]d\sin\theta=n\lambda[/tex]
[tex]y=D\tan\theta[/tex]
[tex]y=D\dfrac{m\lambda}{d}[/tex]
[tex]\lambda=\dfrac{dy}{Dm}[/tex]
Put the value into the formula
[tex]\lambda=\dfrac{0.044\times10^{-3}\times8.1\times10^{-2}}{6.40\times1}[/tex]
[tex]\lambda=5.57\times10^{-7}\ m[/tex]
We need to calculate the frequency
Using formula of frequency
[tex]f =\dfrac{c}{\lambda}[/tex]
[tex]f=\dfrac{3\times10^{8}}{5.57\times10^{-7}}[/tex]
[tex]f=5.4\times10^{14}\ Hz[/tex]
Hence, The wavelength is [tex]5.57\times10^{-7}\ m[/tex]
The frequency is [tex]5.4\times10^{14}\ Hz[/tex]