Question

Visible light is incident perpendicularly on a grating with 315 rulings/mm. What is the longest wavelength that can be seen in the fifth-order diffraction?

Short answer

635nm

Step-by-step solution

Identification of the given data

The given data is listed below as:

• The Grating is 315 rulings/mm .

The condition of the diffraction grating

The condition of the diffraction grating is:

$dsin\theta =m\lambda$$dsin\theta =m\lambda$

Here, d is the distance between adjacent rulings and $\lambda$ is the wavelength of light.

 Step 3: To find the longest wavelength that can be seen in the fifth-order diffraction

For the mth order diffraction maximum, the angular location is given by,

$d\sin \theta =m\lambda$

Now, to find the longest wavelength for the fifth-order diffraction

Let’s assume, $\sin \theta {|}_{m=5}=\raisebox{1ex}{$5\lambda $}\!\left/ \!\raisebox{-1ex}{$d$}\right.<1$.

Or, $\lambda <\frac{d}{5}$

$\begin{array}{l}\lambda =\frac{1nm/315}{5}\\ \lambda =635\mathrm{mm}\end{array}$

Thus,the longest wavelength that can be seen in the fifth order diffraction is 635 nm.