Question

A 6200 line/cm diffraction grating is 3.14 cm wide. If light with wavelengths near 624 nm falls on the grating, how close can two wavelengths be if they are to be resolved in any order

Answer 1

`1.6026299569* 10^(-11)\ m`

Step-by-step explanation:

Grating constant

`d=(1)/(6200)=0.000161\ cm=0.000161* 10^(-2)\ m`

Number of slits

`N=3.14* 6200=19468`

Order

`m=(d)/(\lambda)\\\Rightarrow m=(0.000161* 10^(-2))/(624* 10^(-9))\\\Rightarrow m\approx 2`

At m = 1

`\Delta\lambda=(\lambda)/(mN)\\\Rightarrow \Delta\lambda=(624* 10^(-9))/(1* 19468)\\\Rightarrow \Delta\lambda=3.2052599137* 10^(-11)\ m`

At m = 2

`\Delta\lambda=(\lambda)/(mN)\\\Rightarrow \Delta\lambda=(624* 10^(-9))/(2* 19468)\\\Rightarrow \Delta\lambda=1.6026299569* 10^(-11)\ m`

The wavelengths can be close by
`1.6026299569* 10^(-11)\ m`