Question

Coherent light from a sodium-vapor lamp is passed through a filter that blocks everything except for light of a single wavelength. It then falls on two slits separated by 0.460 mm. In the resulting interference pattern on a screen 2.20 m away, adjacent bright fringes are separated by 2.82 mm. What is the wavelength of the light that falls on the slits

Answer 1

`5.896* 10^(-7)\ \text{m}`

Step-by-step explanation:

D = Distance of the screen from the light source = 2.2 m

d = Distance between slits = 0.46 mm

m = Order

Distance between adjacent bright fringes is 2.82 m

`y_(m+1)-y_m=2.82\ \text{mm}\\\Rightarrow (D(m+1)\lambda)/(d)-(Dm\lambda)/(d)=2.82* 10^(-3)\\\Rightarrow (D\lambda)/(d)(m+1-m)=2.82* 10^(-3)\\\Rightarrow \lambda=(d)/(D)2.82* 10^(-3)\\\Rightarrow \lambda=(0.46* 10^(-3)* 2.82* 10^(-3))/(2.2)\\\Rightarrow \lambda=5.896* 10^(-7)\ \text{m}`

The wavelength of the light that falls on the slits is
`5.896* 10^(-7)\ \text{m}`.