Question

A grating with d = 1.50 mm is illuminated at various angles of incidence by light of wavelength 600 nm. Plot, as a function of the angle of incidence (0 to 90°), the angular deviation of the first order maximum from the incident direction.

Short answer

The graph of the angular deviation is shown below,

Step-by-step solution

Identification of given data

The given data can be listed below,

• The diffraction grating is,$d=15\text{mm}$
• The wavelength of the light is,$\lambda =600\text{nm}$
• The range of angle of incidence is,$0°\text{to}90°$
• The order of angular deviation is, $m=1$

Concept/Significance of diffraction grating

The most effective method for distinguishing light with various frequencies is grating. It is the most crucial element in spectroscopy. A crucial instrument in scientific inquiry is grating's ability to alter the wave vector of incident light.

Determination of the Plot, as a function of the angle of incidence (0 to 90°), the angular deviation of the first order maximum from the incident direction

The angular deviation of the diffracted ray is given by,

$$\begin{gathered} \psi \text{'}=\psi +\theta \\ =\psi +{\sin }^{-1}\left(\frac{\lambda }{d}-\sin \psi \right) \end{gathered}$$

The ratio of$\frac{\lambda }{d}$ is given by the using the brags law,

$d\sin \theta =m\lambda$

Here, dis the inter-planar distance, is the wavelength of light, m is the order of diffraction.

Substitute all the values in the above,

$\frac{\lambda }{d}=0.40$

Thus, the graph of the angular deviation is shown below,