A) \[1\times {{10}^{-6}}\,m\]
B) \[5.2\times {{10}^{-6}}\,m\]
C) \[1.3\times {{10}^{-6}}\,m\]
D) \[2.6\times {{10}^{-6}}\,m\]
Correct Answer: C
Solution :
When rays of monochromatic light of wavelength \[\lambda \] are incident on a diffraction grating in which slit separation is d, then for angle of diffraction 6, the following relation holds true. \[d\,\sin \theta =n\,\lambda \] where n is called the spectrum order. Given, \[n=1,\,\lambda =6500\,\overset{o}{\mathop{A}}\,=6500\times {{10}^{-10}}m\], \[\sin \,{{30}^{o}}=\frac{1}{2}\]. \[\Rightarrow \] \[d=\frac{n\,\lambda }{\sin \theta }\] \[\therefore \] \[d=\frac{6500\times {{10}^{-10}}}{(1/2)}\] \[d=1.3\times {{10}^{-6}}\,\,m\].
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