Answer:
515.5 nm
Explanation:
To find the wavelength (λ) of the laser light we can use the following equation:
[tex] n\lambda = dsin(\theta) [/tex]
Where:
n: is the order of the principal maxima = 1
d: is the width of the groove = 1/N
N: is the number of grooves per length = 5139 grooves/cm
θ: is the angle made by the spectral line → tanθ = D/L
D: is the separation from the wall = 0.488 m
L: is the separation from the grating = 1.78 m
First, we have to find d and θ:
[tex] d = \frac{1}{N} = \frac{1}{5139 grooves/cm}*\frac{1 m}{100 cm} = 1.95 \cdot 10^{-6} m [/tex]
[tex] \theta = arctan(\frac{D}{L}) = arctang (\frac{0.488 m}{1.78 m}) = 15.33 ^\circ [/tex]
Now, we can calculate the wavelength of the laser light:
[tex]\lambda = \frac{dsin(\theta)}{n} = \frac{1.95 \cdot 10^{-6} m*sin(15.33)}{1} = 5.155 \cdot 10^{-7} m = 515.5 nm[/tex]
Therefore, the wavelength of the laser light is 515.5 nm.
I hope it helps you!
