Question

As an admirer of Thomas Young, you perform a double-slit experiment in his honor. You set your slits 1.15 mm apart and position your screen 3.53 m from the slits. Although Young had to struggle to achieve a monochromatic light beam of sufficient intensity, you simply turn on a laser with a wavelength of 639 nm . How far on the screen are the first bright fringe and the second dark fringe from the central bright fringe

Answer 1

Answer:
`y_1=1.9\ mm`

Step-by-step explanation:

Given

slit width
`d=1.15\ mm`

Distance of screen
`D=3.53\ m`

wavelength
`\lambda =639\ nm`

Position of any bright fringe is given by

`y_n=(n\lambda D)/(d)`

`y_1=(1* 639* 10^(-9)* 3.53)/(1.15* 10^(-3))`

`y_1=0.0019\ m`

`y_1=1.9\ mm`

Position of dark fringe is given by

`y_D=((2n+1)\lambda D)/(2d)`

for second dark fringe
`n=1`

`y_D=(1.5* 639* 10^(-9)* 3.53)/(1.15* 10^(-3))`

`y_D=0.00294\ m\approx 2.94\ mm`