Question

a narrow beam of monocromatic lit is incident normally on a diffraction grating third order diffracted beam are formed at an angle of 45 to the original direction.what is the highest order of diffracted beam produced by this grating?

Answer 1

QUESTION:

a narrow beam of monocromatic lit is incident normally on a diffraction grating third order diffracted beam are formed at an angle of 45 to the original direction. what is the highest order of diffracted beam produced by this grating?

SOLUTION:

The diffracted light has maxima at angles $\varphi$ given by

$$d \sin \varphi = m \lambda$$

Here $d$ is grating period, $m$ is order of diffraction and $\lambda$ is wavelength of incident light.

So, the highest order of diffraction:

$$m_{\max} = \frac{d \sin \varphi_{\max}}{\lambda}$$

As diffracted beam is formed at an angle of 45:

$$d \sin 45 = 3 \lambda$$ $$\frac{d}{\lambda} = \frac{3}{\sin 45} = \frac{3 \cdot 2}{\sqrt{2}} = 3 \sqrt{2} \approx 4.24$$

So, the highest order of diffraction is

$$m_{\max} = \frac{d \sin \varphi_{\max}}{\lambda} = 4.24 \cdot \sin \varphi_{\max}$$ $$m_{\max} = 4 \quad \text{(because } |\sin \varphi| \leq 1\text{)}$$

ANSWER:

4