Answer:
The separation between third order and first order is 0.0304 m
Explanation:
Given:
Separation between two slit [tex]d = 0.0580 \times 10^{-3}[/tex] m
Distance between slit and screen [tex]D = 1.50[/tex] m
Wavelength of light [tex]\lambda = 588 \times 10^{-9}[/tex] m
From the formula of interference of light,
[tex]d \sin \theta = n\lambda[/tex]
Here [tex]\sin \theta = \frac{x}{D}[/tex]
[tex]\frac{dx}{D} = n \lambda[/tex]
[tex]x = \frac{n\lambda D}{d}[/tex]
Where [tex]x =[/tex] separation between fringes
Here we have to find between third order and first order,
[tex]x = \frac{(n_{3} - n_{1})\lambda D }{d}[/tex]
Where [tex]n_{3}[/tex] = 3 [tex]n_{1}[/tex] = 1
[tex]x = \frac{2 \times 588 \times 10^{-9} \times 1.50}{0.0580 \times 10^{-3} }[/tex]
[tex]x = 0.0304[/tex] m
Therefore, the separation between third order and first order is 0.0304 m
