Visible light passes through a diffraction grating that has 900 slits per centimeter, and the interference pattern is observed on a screen that is 2.78 m from the grating. In the first-order spectrum, maxima for two different wavelengths are separated on the screen by 2.66 mm . What is the difference between these wavelengths? Express your answer in meters.

Respuesta :

Answer:[tex]0.62\times 10^{-8}=10.62 nm[/tex]

Explanation:

Given

No of lines in the grating (N)=900 slits per centimeter

Distance between screen and grating(L)=2.78 m

Slit width(d) =[tex]\frac{1}{N}=1.11\times 10^{-5}m[/tex]

We know distance between two maxima

[tex]\dealta y=\left ( \frac{\lambda _1-\lambda _2}{d}\right )L[/tex]

therefore

[tex]\lambda _1-\lambda _2=\frac{d\delta y}{L}[/tex]

[tex]\lambda _1-\lambda _2=\frac{1.11\times 10^{-5}\times 2.66\times 10^{-3}}{2.78}[/tex]

[tex]\lambda _1-\lambda _2=10.62\times 10^{-8}=10.62 nm[/tex]

ACCESS MORE
EDU ACCESS