Question

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?

Answer 1

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

$d=\dfrac{2\times10^{-2}}{10000}$

$d=0.000002\ m$

We need to calculate the wavelength of this starlight

Using formula of distance

$d\sin\theta=n\lambda$

$\lambda=\dfrac{d\sin\theta}{m}$

Put the value into the formula

$\lambda=\dfrac{2\times10^{-6}\sin45}{2}$

$\lambda=707\times10^{-9}\ m$

$\lambda=707\ nm$

Hence, The wavelength of this starlight is 707 nm.