In Young's double-slit experiment, the distance between the first minima on the screen (the distance between the central maximum and the first minimum on either side) is equal to the wavelength of the light divided by the separation between the slits. Therefore, if the distance between the slits 'd' is twice the distance between the screen and the slits 'D', then the distance between the first minima on the screen will be 2D = Nλ/d, where N is the number you are trying to find.
Since the distance between the first minima on the screen is also given as D, we can set up the equation 2D = Nλ/d = D. Solving for N, we find that N =d/(λ/D)=dD/λ. In this case, the value of d is 2D, so
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Answer:
N = 9.93
Explanation:
In Young's double-slit experiment, the distance between the first minima on the screen (the distance between the central maximum and the first minimum on either side) is equal to the wavelength of the light divided by the separation between the slits. Therefore, if the distance between the slits 'd' is twice the distance between the screen and the slits 'D', then the distance between the first minima on the screen will be 2D = Nλ/d, where N is the number you are trying to find.
Since the distance between the first minima on the screen is also given as D, we can set up the equation 2D = Nλ/d = D. Solving for N, we find that N =d/(λ/D)=dD/λ. In this case, the value of d is 2D, so
[tex]\rm{N = (2D)\dfrac{D}{\lambda} = 2\dfrac{D²}{\lambda}} \\ [/tex]
Substituting the values of D given in the problem,we find that
[tex]\rm{N = 2\dfrac{\bigg(N\frac{\lambda}{2}\bigg)^{2}}{\lambda} = 4 \dfrac{N²}{\lambda}} \\ [/tex]
Since, the value of √5 is given as 2.24, we can substitute this into the equation to find that
[tex]\rm{N = 4\dfrac{2.24^{2}}{1} = \bf{9.93}}[/tex]
Therefore, the value of N is this case is approx. 9.93.
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