Answer:
The wavelength is 539 nm.
Explanation:
Given that,
Distance of screen L= 10 m
Width s= 5.4 cm
Grating separation d= 0.1 mm
Suppose the pattern is displayed on a screen a distance L from the grating and the spots are separated by s. we need to find the wavelength.
The angle between the central and first maximum is given as
[tex]\tan\theta=\dfrac{s}{L}[/tex]
[tex]\theta=\tan^{-1}\dfrac{s}{L}[/tex]
[tex]\theta=\tan^{-1}\dfrac{5.4\times10^{-2}}{10}[/tex]
[tex]\theta=0.309[/tex]
We need to calculate the wavelength
The condition for maximum of a diffraction grating is
[tex]d\sin\theta=m\lambda[/tex]
[tex]\lambda=\dfrac{d\sin\theta}{m}[/tex]
Put the value into the formula
[tex]\lambda=\dfrac{0.1\times10^{-3}\times\sin0.309}{1}[/tex]
[tex]\lambda=539\times10^{-9}\ m[/tex]
[tex]\lambda=539\ nm[/tex]
Hence, The wavelength is 539 nm.
