Respuesta :
Answer:
The difference between these wavelengths is 15.85 nm.
Explanation:
Given that,
The number of lines on the grating N= 900 cm
Distance between screen grating L= 2.24 m
Order number = 1
Distance y = 3.20 mm
We need to calculate the width of the slit
Using formula of width
[tex]d=\dfrac{1}{N}[/tex]
Put the value into the formula
[tex]d=\dfrac{1}{900}[/tex]
[tex]d =0.00111 = 1.11\times10^{-5}\ m[/tex]
We need to calculate the angular distance
[tex]\theta=\dfrac{\lambda}{d}[/tex]
The angular separation for different wavelength is
[tex]\Delta \theta=\dfrac{\lambda_{1}-\lambda_{2}}{d}[/tex]
We know that,
Linear separation is
[tex]\Delta y = \Delta \theta L[/tex]
We nee to calculate the difference between these wavelengths
Put the value into the formula of angular separation
[tex]\Delta y=L(\dfrac{\lambda_{1}-\lambda_{2}}{d})[/tex]
[tex]\lambda_{1}-\lambda_{2}=\dfrac{\Delta y\times d}{L}[/tex]
[tex]\lambda_{1}-\lambda_{2}=\dfrac{3.20\times10^{-3}\times1.11\times10^{-5}}{2.24}[/tex]
[tex]\lambda_{1}-\lambda_{2}=1.585\times10^{-8}[/tex]
[tex]\lambda_{1}-\lambda_{2}=15.85\ nm[/tex]
Hence, The difference between these wavelengths is 15.85 nm.
