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]