Question

Light with a single wavelength falls on two slits separated by 0.510 mm. In the resulting interference pattern on a screen 2.24 m away, adjacent bright fringes are separated by 2.88 mm.What is the wavelength of the light that falls on the slits

Answer 1

Answer: 655.7 nm

Explanation:

Given

The slits are separated by $d=0.510\ mm$

Distance between slits and screen is $D=2.24\ m$

Adjacent bright fringes are $\beta =2.88\ mm$ apart

Also, the distance between bright fringes is given by  

$\Rightarrow \beta =\dfrac{\lambda D}{d}\quad [\lambda=\text{Wavelength of light}]\\\\\text{Insert the values}\\\\\Rightarrow 2.88\times 10^{-3}=\dfrac{\lambda \cdot 2.24}{0.510\times 10^{-3}}\\\\\Rightarrow \lambda =\dfrac{2.88\times 10^{-3}\times 0.510\times 10^{-3}}{2.24}\\\\\Rightarrow \lambda =0.6557\times 10^{-6}\ m\\\Rightarrow \lambda =655.7\ nm$