Question

compute the angular dispersion of a 600 lines per mm amplitude grating at 400 nm. assume you are working in first order and that the angle of incidence is 25 degrees.

Answer 1

The angular dispersion of a 600 lines per mm amplitude grating at 400 nm is 45 degrees.

To compute the angular dispersion of a 600 lines per mm amplitude grating at 400 nm, we can use the following formula:

`$$\theta = (12\pi)/(n\lambda)$$`

where
`$\theta$` is the angular dispersion,
`$n$` is the grating constant (600 lines/mm), and
`$\lambda$` is the wavelength of light (400 nm). Plugging in the values, we get:

`$$\theta = (12\pi)/(600 * 400) = (12\pi)/(2400) = (3\pi)/(200)$$`

Thus, the angular dispersion for a 600 lines per mm amplitude grating at 400 nm is:

`$$\theta = (3\pi)/(200) = (3)/(4)$$`

In degrees, this is:

`$$\theta = (3)/(4) * (180)/(\pi) = 45^\circ$$`

So, the angular dispersion of a 600 lines per mm amplitude grating at 400 nm is 45 degrees.

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