The two most prominent wavelengths in the light emitted by a hydrogen discharge lamp are 656 nm (red) and 486 nm (blue). Light from a hydrogen lamp illuminates a diffraction grating with 500 lines/mm, and the light is observed on a screen 1.50 m behind the grating. What is the distance between the first-order red and blue fringes?

Young's experiment is used to find the distance of n'th number dark fringe from the central fringe of the screen. It can be found out with the following formula given as,

[tex]d\sin\theta=m\lambda[/tex]

Here, (λ) is the wavelength of the light and (d) is the distance of the screen to the slits.

The two most prominent wavelengths in the light emitted by a hydrogen discharge lamp are 656 nm (red) and 486 nm (blue).

Light from a hydrogen lamp illuminates a diffraction grating with 500 lines/mm. Thus, the value of distance will be,

[tex]d=\dfrac{1}{500}\\d=2\times10^{-3} \rm\; mm[/tex]

For the red light, the value of the angle is,

[tex](2\times10^{-6})\sin\theta=(1)(656\times10^{-9})\\\theta=19.15^o[/tex]

The light is observed on a screen 1.50 m behind the grating. The distance of the red light,

[tex]Y=(1.5)\tan(19.15)\\Y=0.521\rm m[/tex]

For the blue light, the value of the angle is,

[tex](2\times10^{-6})\sin\theta=(1)(486\times10^{-9})\\\theta=14.06^o[/tex]

The distance of the blue light,

[tex]Y=(1.5)\tan(14.06)\\Y=0.376\rm m[/tex]

The distance between the first-order red and blue fringes is,

[tex]d=0.521-0.376\\d=0.145\rm\; m[/tex]

Thus, the distance between the first-order red and blue fringes is 0.145 meters.

Learn more about the young's experiment here;

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