Answer:
a
[tex]y_1 = 0.004589 \ m[/tex]
b
[tex]y_2 =0.009179 \ m[/tex]
Explanation:
From the question we are told that
The wavelength of the red light is [tex]\lambda _r = 633 \ nm = 633 *10^{-9} \ m[/tex]
The width of the slit is [tex]d = 0.40 mm = 0.40 *10^{-3} \ m[/tex]
The distance of the screen from the point of diffraction is [tex]D = 2.9 \ m[/tex]
Generally the width of the central bright fringe is mathematically represented as
[tex]y_1 = \frac{\lambda * D}{d}[/tex]
=> [tex]y_1 = \frac{633 *10^{-9} * 2.90 }{0.40 *10^{-3}}[/tex]
=> [tex]y_1 = 0.004589 \ m[/tex]
Generally the width of the first bright fringe on either side of the central one is mathematically represented as
[tex]y_2 = 2 * y_1[/tex]
=> [tex]y_2 = 2 * 0.004589[/tex]
=> [tex]y_2 =0.009179 \ m[/tex]