Question

A light with a second-order dark band forms a diffraction angle of 20.0 degrees. The diffraction grating has 200.0 lines per mm. The wavelength of the light, to the nearest whole number, is _____ nm.

Answer 1

The value is
`\lambda = 684 \ nm`

Step-by-step explanation:

From the question we are told that

The order of the dark fringe is m = 2

The diffraction angle is
`\theta = 20^o`

The diffraction grating is
`l = 200\ lines\ per\ mm \ = \ 200000\ lines\ per\ m`

Generally separation between the slits is mathematically represented as

`d = (1)/( 200000)`

=>
`d = 5 *10^( -6) \ m`

Generally the condition for destructive interference is mathematically represented as

`dsin(\theta ) = (m - (1)/(2) ) \lambda`

=>
`5 *10^(-6) sin(20) = [2 + (1)/(2)] * \lambda`

=>
`\lambda = 684 *10^(-9) \ m`

=>
`\lambda = 684 \ nm`