A spectrometer with grating size of 2 cm and a total of 10,000 lines is used to analyze the spectrum of a star. The light is normally incident on the grating and illuminates the whole grating. A sharp spectral line is observed in second order at an angle of 45o from normal incidence. What is the wavelength of this starlight?

Respuesta :

Answer:

The wavelength of this starlight is 707 nm.

Explanation:

Given that,

Distance = 2 cm

Total lines = 10000

Angle = 45°

We need to calculate the distance

[tex]d=\dfrac{2\times10^{-2}}{10000}[/tex]

[tex]d=0.000002\ m[/tex]

We need to calculate the wavelength of this starlight

Using formula of distance

[tex]d\sin\theta=n\lambda[/tex]

[tex]\lambda=\dfrac{d\sin\theta}{m}[/tex]

Put the value into the formula

[tex]\lambda=\dfrac{2\times10^{-6}\sin45}{2}[/tex]

[tex]\lambda=707\times10^{-9}\ m[/tex]

[tex]\lambda=707\ nm[/tex]

Hence, The wavelength of this starlight is 707 nm.

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