Question

Why the rays must fall on the grating surface normally in measurement of laser wavelength?

Answer 1

Answer on Question #46039, Physics, Optics

Why the rays must fall on the grating surface normally in measurement of laser wavelength?

Answer:

When light is normally incident on the grating, the diffracted light will have maxima at angles $\theta$ given by:

$$d \sin \theta = n \lambda$$

where $n =$ the order of the image (0, 1, 2...)

$d =$ the distance between two lines of the grating

$\theta =$ the angular position of the image (measured from the normal to the grating)

By measuring D and y, $\theta$ can be found.

We can then calculate the wavelength, $\lambda$

$$\lambda = \frac {d \sin \theta}{n}$$

If a plane wave is incident at any arbitrary angle $\theta_{\mathrm{i}}$ , the grating equation becomes:

$$d (\sin \theta + \sin \theta_ {i}) = n \lambda$$

Thus, in that case to obtain the wavelength $\lambda$ we need to solve equation

$$\lambda = \frac {d (\sin \theta + \sin \theta_ {i})}{n}$$

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