Answer:
0.000109375 m
Explanation:
d = Distance between grating = 0.5 mm
m = Order
[tex]\lambda_1=\dfrac{d}{8}[/tex]
Minima relation
[tex]m-\dfrac{1}{2}[/tex]
For fourth order minima
[tex]dsin\theta=(4-\dfrac{1}{2})\lambda_1[/tex]
For second maxima
[tex]dsin\theta=2\lambda_2[/tex]
From the two equations we get
[tex](4-\dfrac{1}{2})\lambda_1=2\lambda_2\\\Rightarrow \lambda_2=\dfrac{(4-\dfrac{1}{2})\lambda_1}{2}\\\Rightarrow \lambda_2=\dfrac{(4-\dfrac{1}{2})\dfrac{0.5\times 10^{-3}}{8}}{2}\\\Rightarrow \lambda_2=0.000109375\ m[/tex]
The wavelength is 0.000109375 m
Wavelength is the distance between two successive crest of a wave. the the wavelength λ of the second laser that would place its second maximum is 0.109375 mm.
The equation for double slit interference (constructive) can be given as,
[tex]d\sin \theta =m\lambda[/tex]
Here, (m) is the order, λ is the wavelength and (d) is the distance between the slit.
Given information-
The wavelength of the laser is d/8.
The distance of the slit separation is 0.500 mm.
Put the value of distance to find the values of wavelength as,
[tex]\lambda_1=\dfrac{0.5\times10^{-3}}{8}\\\lambda_1=0.0625\times10^{-3}[/tex]
As the wavelength of the second laser that would place its second maximum at the same location as the fourth minimum of the first laser.
Thus first we have to find the forth order minima as,
[tex]d\sin \theta=(4-\dfrac{1}{2} )\lambda_1\\d\sin \theta=(\dfrac{7}{2} )\lambda_1\\[/tex] .......1
The second maxima can be given as,
[tex]d\sin \theta=2\lambda_2\\[/tex]
Put the value of [tex]d\sin\theta[/tex] in the above equation as,
[tex]\dfrac{7}{2}\lambda_1=2\lambda_2\\\dfrac{7}{2}\times(0.0625\times10^{-3})=2\lambda_2\\\lambda_2=0.000109375\rm m\\\lambda_2=0.109375\rm mm\\[/tex]
Hence, the the wavelength λ of the second laser that would place its second maximum is 0.109375 mm.
Learn more about the constructive interference here;
https://brainly.com/question/1040831
