In a spectrometer experiment, monochromatic light is incident normally on a diffraction grating having `4.5xx10^5` lines per metre. The seond order line is seen at an angle of `30^@` to the normal. What is the wavelength of the light?

Options

A. (a) `200nm`
B. (b) `556nm`
C. (c) `430nm`
D. (d) `589nm`

Answer

B

Explanation

The angle of diffraction `theta` normal to the grating for `n^(th)` order diffraction pattern is given by `dsintheta=nlambda`
Where `d` is the spacing of the slits
`lambda` is the wavelength of the source.
Now `d=(1)/(4.5xx10^5)m`, `theta=30^@` and `n=2`
We thus have `lambda=(dsintheta)/(n)=(sin30^@)/(2(4.5xx10^5))=566m`