light

[logistic_guy]

At what angle will \(\displaystyle 440\)-\(\displaystyle \text{nm}\) light produce a third-order maximum when falling on a grating whose slits are \(\displaystyle 1.35 \times 10^{-3} \ \text{cm}\) apart?

 

[khansaheb]

At what angle will \(\displaystyle 440\)-\(\displaystyle \text{nm}\) light produce a third-order maximum when falling on a grating whose slits are \(\displaystyle 1.35 \times 10^{-3} \ \text{cm}\) apart?

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING​

Please share your work/thoughts about this problem

 

[logistic_guy]

We use the diffraction maxima formula.

\(\displaystyle d\sin \theta = m\lambda\)

Third-order means \(\displaystyle m = 3\), then

\(\displaystyle 1.35 \times 10^{-5}\sin \theta = 3(440 \times 10^{-9})\)

This gives:

\(\displaystyle \sin\theta = 0.0977778\)

\(\displaystyle \theta = \sin^{-1} 0.0977778 = 5.61^{\circ}\)