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

The wavelength of this starlight is 707 nm.

Step-by-step explanation:

Given that,

Distance = 2 cm

Total lines = 10000

Angle = 45°

We need to calculate the distance

`d=(2*10^(-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=(d\sin\theta)/(m)`

Put the value into the formula

`\lambda=(2*10^(-6)\sin45)/(2)`

`\lambda=707*10^(-9)\ m`

`\lambda=707\ nm`

Hence, The wavelength of this starlight is 707 nm.