Answer:
[tex]9.07443\times 10^{-6}\ m[/tex]
Explanation:
d = Spacing between slits of the grating
[tex]\lambda[/tex] = Wavelength = 633 nm
As there are two bright fringes they will equally dispose on the screen from the central point
[tex]\dfrac{0.35}{2}=0.175\ m[/tex]
We have the relation
[tex]tan\theta=\dfrac{0.175}{2.5}\\\Rightarrow \theta=tan^{-1}\dfrac{0.175}{2.5}\\\Rightarrow \theta=4^{\circ}[/tex]
Wavelength is given by
[tex]\lambda=dsin\theta\\\Rightarrow d=\dfrac{\lambda}{sin\theta}\\\Rightarrow d=\dfrac{633\times 10^{-9}}{sin4}\\\Rightarrow d=9.07443\times 10^{-6}\ m[/tex]
The spacing between slits of the grating is [tex]9.07443\times 10^{-6}\ m[/tex]