Monochromatic light of wavelength 500 nm is incident normally on a diffraction grating.If the third-order maximum of the diffraction pattern is observed at 32.0° from the central spot,how many TOTAL number of maxima can be seen?

Question

Quizplus · Accepted Answer

The angular position $	heta_m$ of the maxima is given by the equation:

$$d\sin(	heta_m)=m\lambda$$

where $d$ is the grating spacing, $\lambda$ is the wavelength, and $m$ is the order of the maximum.

For the third-order maximum, we have:

$$d\sin(	heta_3)=3\lambda$$

Since we know the wavelength and the angle, we can solve for the grating spacing:

$$d=\frac{3\lambda}{\sin(	heta_3)}=\frac{3(500\ \mathrm{nm})}{\sin(32.0^\circ)}\approx1130\ \mathrm{nm}$$

The total number of maxima that can be seen is given by:

$$N=\frac{L}{d}+1$$

where $L$ is the length of the grating (which we can assume to be infinite). Plugging in the values, we get:

$$N=\frac{\infty}{1130\ \mathrm{nm}}+1=\infty$$

But in practice, the number of maxima that can be seen is limited by the resolving power of the human eye and the intensity of the diffracted light. Typically, we can see up to about 10-20 maxima. Therefore, the closest answer choice is D) 11.

Monochromatic Light of Wavelength 500 Nm Is Incident Normally on a Diffraction