Answer:
Explanation:
Given
wavelength [tex]\lambda =633\ nm[/tex]
distance between two slits [tex]d=0.5\ mm[/tex]
Screen is placed at a distance [tex]L=2.5\ m[/tex]
Location of a (n+1)th bright fringe is given by
[tex]x_{n+1}=\frac{L}{2d}(n+1)\lambda [/tex]
for nth bright fringe
[tex]x_n=\frac{L}{2d}(n)\lambda [/tex]
Distance between two bright fringes
[tex]x_{n+1}-x_n=\frac{L}{2d}\cdot \lambda [/tex]
[tex]x_{n+1}-x_n=\frac{2.5}{2\times 0.5\times 10^{-3}}\cdot 633\times 10^{-3}[/tex]
[tex]x_{n+1}-x_n=1.582\ mm[/tex]
Bright fringes are created from light rays.
The spacing between two adjacent bright fringes is 0.0015825m
The given parameters are:
[tex]\mathbf{\lambda = 633nm}[/tex]
[tex]\mathbf{d =0.50mm}[/tex]
[tex]\mathbf{L =2.50m}[/tex]
For a bright fringe, the location is calculated as:
[tex]\mathbf{x_{n + 1} = \frac{L}{2d}(n + 1)\lambda}[/tex]
Replace n + 1 with n
[tex]\mathbf{x_{n} = \frac{L}{2d}(n)\lambda}[/tex]
Subtract both equations
[tex]\mathbf{x_{n + 1} - x_{n} = \frac{L}{2d}(n + 1)\lambda - \frac{L}{2d}(n)\lambda}[/tex]
Factorize
[tex]\mathbf{x_{n + 1} - x_{n} = \frac{L}{2d}(n + 1 -n)\lambda }[/tex]
[tex]\mathbf{x_{n + 1} - x_{n} = \frac{L}{2d}(1)\lambda }[/tex]
[tex]\mathbf{x_{n + 1} - x_{n} = \frac{L}{2d}\lambda }[/tex]
Substitute known values
[tex]\mathbf{x_{n + 1} - x_{n} = \frac{2.50m}{2 \times 0.50mm}(n)\times 633nm}\\[/tex]
Convert to meters
[tex]\mathbf{x_{n + 1} - x_{n} = \frac{2.50m}{2 \times 0.50 \times 0.001m}\times 633 \times 0.000000001 m}[/tex]
[tex]\mathbf{x_{n + 1} - x_{n} = \frac{2.50m\times 633 \times 0.000000001}{0.001} }[/tex]
[tex]\mathbf{x_{n + 1} - x_{n} = 0.0015825m }[/tex]
Hence, the spacing between two adjacent bright fringes is 0.0015825m
Read more about bright fringes at:
https://brainly.com/question/12732324
