Question

What is the wavelength in nm of a light whose first order bright band forms a diffraction angle of 30 degrees, and the diffraction grating has 700 lines per mm?

Answer 1

Answer: 714.285 nm

Explanation:

The diffraction angles $\theta_{n}$ when we have a slit divided into $n$ parts are obtained by the following equation:  

$d sin\theta_{n}=n \lambda$ (1)  

Where:  

$d$ is the width of the slit  

$\lambda$ is the wavelength of the light  

$n$ is an integer different from zero

Now, the first-order diffraction angle is given when $n=1$, hence equation (1) is rewritten as:  

$dsin\theta_{1}=\lambda$ (2)  

We know:  

$\theta_{1}=30\°$  

In addition we are told the diffraction grating has 700 lines per mm, this means:  

$d=\frac{1mm}{700}$  

Solving (2) with the known values we will find $\lambda$:  

$\lambda=(\frac{1mm}{700})sin(30\°)$ (3)  

$\lambda=0.000714285 mm$ (4)  

Knowing $1mm=10^{6}nm$:

$\lambda=714.285 nm$ This is the wavelength of the light