Question

in young's double slit experiment wavelength of light used is 5000 M and stars and distance between the slits his to millimetre distance of screen from this lady is 1 m find the fringe width and also the calculate the distance of 7th dark fringe from the central bright fringe ​

Answer 1

Given,

wavelength of light used, λ = 5000A° = 5000 x 10⁻¹⁰ = 5 x 10⁻⁷

distance between the slits, d = 2 mm = 2 x 10⁻³ m

distance of the screen from the slits, D = 1 m

Hence fringe width is given by,

X = λD/d

=> X = (5 x 10⁻⁷ x 1)/(2 x 10⁻³)

=> X = 2.5 x 10⁻⁴ = 0.25 x 10⁻³ = 0.25 mm

Hence the fringe width will be 0.25 mm

Distance of the dark fringes is given by,

xₙ = (2n-1)λD/2d

So the distance of the 7th dark fringe is given by,

x₇ = (14-1) x 0.25/2 mm                    (as λD/d = 0.25 mm)

=> x₇ = 6.5 x 0.25 = 1.625 mm

Hence the distance of 7th dark fringe from central bright fringe will be  1.625 mm