Respuesta :
Answer:
641 nm.
Explanation:
Given that,
A transmission grating has 5200 slits/cm.
We need to find the longest wavelength that can be observed in the third order. Using grating equation as follows :
[tex]d\sin\theta=m\lambda[/tex] ...(1)
d is slit spacing
No fo slit per unit length :
[tex]N={5200}\ slit/cm\\\\=520000\ slits/m[/tex]
We know that, N = 1/d
For longest wavelength, θ = 90°
From equation (1)
[tex]\dfrac{\sin\theta}{m\lambda}=\dfrac{1}{d}\\\\520000=\dfrac{\sin(90)}{3\lambda}\\\\\lambda=\dfrac{1}{520000\times 3}\\\\=6.41\times 10^{-7}\ m\\\\=641\ nm[/tex]
Hence, the longest wavelength in third order for a transmission grating is 641 nm.
