Answer:
[tex] 2.77[/tex] cm
Explanation:
[tex]d[/tex] = separation between the slits = 2783 x 10⁻⁹ m
[tex]\lambda[/tex] = wavelength of coherent light = 644 nm = 644 x 10⁻⁹ m
[tex]D[/tex] = Distance of the screen = 6 cm = 0.06 m
[tex]y_{n}[/tex] = Position of nth bright fringe
Position of nth bright fringe is given as
[tex]y_{n} = \frac{nD\lambda }{d}[/tex]
for n = 2
[tex]y_{2} = \frac{nD\lambda }{d}[/tex]
[tex]y_{2} = \frac{(2)(0.06)(644\times10^{-9}))}{2783\times10^{-9}}[/tex]
[tex]y_{2} = 0.0278[/tex] m
for n = 4
[tex]y_{4} = \frac{nD\lambda }{d}[/tex]
[tex]y_{4} = \frac{(4)(0.06)(644\times10^{-9}))}{2783\times10^{-9}}[/tex]
[tex]y_{4} = 0.0555[/tex] m
Distance between 4th and 2nd bright fringes is given as
[tex]w = y_{4} - y_{2} = 0.0555 - 0.0278 = 0.0277 m[/tex]
[tex]w = 2.77[/tex] cm
