Answer:
60.46°
Explanation:
Given that, the wavelength of yellow light which is falling on grating is,
[tex]\lambda=580 nm\\\lambda=580\times 10^{-9}m[/tex]
The angle is of the order of 3 means m=3.
And number of lines per mm is,
[tex]N=500\frac{lines}{mm}\\N=(500\times 10^{3})\frac{lines}{m}[/tex]
Therefore the condition of maxima,
[tex]m\lambda=dsin\theta[/tex]
Here, [tex]d=\frac{1}{N}[/tex]
And for third order maxima, m=3
[tex]3\lambda=\frac{1}{N} sin\theta\\sin\theta=3 \lambda N[/tex]
Therefore,
[tex]sin\theta=3\times 580\times 10^{-9}m\times 500\times 10^{3}m\\sin\theta=0.87\\\theta=sin^{-1} (0.87)\\\theta=60.46^{\circ}[/tex]
Therefore, the angle for third order maxima is 60.46°.
