The spacing between adjacent slits on a diffraction grating is 3 $\lambda$ .The deviation $\theta$ of the first order diffracted beam is given by:
A)sin($\theta$/2)= 1/3
B)sin($\theta$/3)= 2/3
C)sin($\theta$)= 1/3
D)tan($\theta$/2)= 1/3
E)tan($\theta$)= 2/3

Question

The spacing between adjacent slits on a diffraction grating is 3 $\lambda$ .The deviation  $\theta$ of the first order diffracted beam is given by:
A)sin($\theta$/2)= 1/3
B)sin($\theta$/3)= 2/3
C)sin($\theta$)= 1/3
D)tan($\theta$/2)= 1/3
E)tan($\theta$)= 2/3

Quizplus · Accepted Answer

The formula for the angle of diffraction $\theta$ in a diffraction grating is given by $d\sin(\theta) = m\lambda$, where $d$ is the spacing between the slits, $\lambda$ is the wavelength of the light, and $m$ is the order of the diffracted beam. Given that the spacing $d$ is equal to the wavelength $\lambda$, for the first order ($m=1$), the equation simplifies to $\sin(\theta) = 1/3$, which matches choice C.

The Spacing Between Adjacent Slits on a Diffraction Grating Is λ\lambdaλ

The Spacing Between Adjacent Slits on a Diffraction Grating Is $\lambda$