Question

Calculate the angle for the third-order maximum of 580-nm wavelength yellow light falling on double slits separated by 0.100 mm.

Short answer

The angle for the third-order maximum for the yellow light is${}^{0.997°}$

Step-by-step solution

Given data

The wavelength of the yellow light is ${}^{\mathrm{\lambda }=580\mathrm{nm}\left(\frac{{10}^{-0}\mathrm{m}}{1\mathrm{nm}}\right)=5.8\times {10}^{-7}\mathrm{m}}$

The separation of the double slits is $\mathrm{d}=0.100\mathrm{mm}\left(\frac{1\mathrm{m}}{1000\mathrm{mm}}\right)=1\times {10}^{-4}\mathrm{m}$

Finding the angle which is the third-order maximum

A formula for the angle of the third-order maximum can be expressed as,

$\mathrm{d}\sin \mathrm{\theta }=3\mathrm{\lambda }$………………………….(1)

Substituting the given data in equation (1), we get,

$$\begin{gathered} 1\times {10}^{-4}m)\times \sin \theta =3\times (5.8\times {10}^{-7}m) \\ \theta ={\sin }^{-1}\left(\frac{1.74\times {10}^{-6}m}{1\times {10}^{-4}m}\right) \\ \theta =0.997° \end{gathered}$$

Therefore, the angle for the third order of maxima is $0.997°$.