Question

Light containing two different wavelengths passes through a diffraction grating with 1,250 slits/cm. On a screen 17.5 cm from the grating, the third-order maximum of the shorter wavelength falls midway between the central maximum and the first side maximum for the longer wavelength. If the neighboring maxima of the longer wavelength are 8.44 mm apart on the screen, what are the wavelengths in the light

Answer 1

`\lambda_s =6.43*10^-4m`

Step-by-step explanation:

From the question we are told that:

Diffraction grating
`N=1250slits/cm`

Distance b/w Screen and grating length
`d_(sg)=17.5 cm`

Distance b/w neighboring maxima and Screen
`d_(ms)=8.44`

Generally the equation for grating space is mathematically given by

`d(g)=(1)/(N)`

`d(g)=(100)/(1250)`

`d(g)=0.08`

Generally the equation for small angle approximation is mathematically given by

`\triangle y=(\lambda d)/(L)`

Therefore for longest wavelength

`\lambda _l=(8.44*10^(-3)*(0.08))/(0.175m)`

`\lambda _l=3.858*10^(-3)`

Therefore the third order maximum equation for the shorter wavelength as

`\lambda_s =(1)/(6) \lambda_l`

`\lambda_s =(1)/(6) (3.858*10^-^3)`

`\lambda_s =6.43*10^-4m`

The wavelengths in the light is given as

`\lambda_s =6.43*10^-4m`