Question

light of wavelength 550 nm is incident on a diffraction grating that is 1 cm wide and has 1000 slits. What is the dispersion of the m = 2 line?

Answer 1

The dispersion is
`D = 2.01220 *10^(5) \ rad/m`

Step-by-step explanation:

From the question we are told that

The wavelength of the light is
`\lambda = 550 \ = 550 *10^(-9) \ n`

The width of the grating is
`k = 1\ cm = 0.01 \ m`

The number of slit is N = 1000 slits

The order of the maxima is m = 2

Generally the spacing between the slit is mathematically represented as

`d = (k)/(N)`

substituting values

`d = ( 0.01)/(1000)`

`d = 1.0 *10^(-5) \ m`

Generally the condition for constructive interference is

`d\ sin(\theta ) = m * \lambda`

substituting values

`1.0 *10^(-5) sin (\theta) = 2 * 550 *10^(-9)`

`\theta = sin^(-1) [( 2 * 550 *10^(-9))/( 1.0 *10^(-5)) ]`

`\theta = 6.315^o`

Generally the dispersion is mathematically represented as

`D = ( m )/(d cos(\theta ))`

substituting values

`D = ( 2 )/( 1.0 *10^(-5) cos(6.315 ))`

`D = 2.01220 *10^(5) \ rad/m`