Question

light of wavelength 600nm that falls on a pair of slits producing interference pattern on a screen in which the bright fringes are separated by 7.2mm. what must be the wavelength of another light which is produces bright fringes separated by 8.1mm with the same apparatus?​

Answer 1

Answer:

675 nm

Explanation:

As we know,

β = λd/D   (works for both dark and bright fringes)

Where β = fringe width

λ = wavelength of wave.

d= distance between slits

D= Distance between screen and slits.

Now,

For wave with 600 nm,

$\\\tt \beta = \dfrac{(6 \times 10^{-7})d}{D} = 7.2mm$       -----------(i)

Let the wavelength of another wave be $\lambda_{1}$

$\\\tt \beta_{1} = \dfrac{\lambda_{1} d}{D} =8.1mm$                -----------(ii)

Dividing (i) by (ii)

$\\\tt \dfrac{(6 \times 10^{-7})}{ \lambda_{1}} = \dfrac{7.2}{8.1} \\\lambda_{1} = 6 \times 10^{-7} \times \dfrac{8.1}{7.2} = 6.75 \times 10^{-7} \\ = 675 nm$