Question

A new experiment is created with the screen at a distance of 1.9 m from the slits (with spacing 0.11 mm). What is the distance between the second order bright fringe of light with λ = 695 nm and the third order bright fringe of light with λ = 407 nm? (Give the absolute value of the smallest possible distance between these two fringes: the distance between bright fringes on the same side of the central bright fringe.) |x| =

Answer 1

The distance between the bright fringes is 2.19 mm

Step-by-step explanation:

Distance of the screen from the slits, d = 1.9 m

Slit width, w = 0.11 mm =
`0.11* 10^(- 3)\ m`

Wavelength,
`\lambda = 695\ nm`

Wavelength,
`\lambda' = 407\ nm`

To calculate the distance between the second order bright fringe:

`y_(n) = (n\lambda d)/(w)`

`y'_(3) = (n\lambda' d)/(w) = (3* 695* 10^(- 9)* 1.9)/(0.11* 10^(- 3)) = 0.036\ m`

`y_(2) = (2* 407* 10^(- 9)* 1.9)/(0.11* 10^(- 3)) = 0.014\ m`

Distance, |x| =
`y'_(3) - y_(2)`

|x| =
`0.036 - 0.0141 = 0.0219 m = 2.19\ mm`