KVPY Sample Paper KVPY Stream-SX Model Paper-27

When the diffraction pattern from a certain slit illuminated with laser light \[\text{(}\lambda =6330A{}^\circ \text{)}\]is projected on a screen 150 cm from the slit, the second minima on each side are separated by 8 cm. This tells us that:

A) The slit is approximately 0.005 cm wide

B) The slit is approximately 0.05 cm wide

C) \[\operatorname{a}/\lambda \] is approximately 7.5 (a is the slit width)

D) \[\operatorname{a}/\lambda \] is approximately 750

Correct Answer: A

Solution :

\[\sin {{\theta }_{2}}=\frac{2\lambda }{d}\] Or\[{{\theta }_{2}}={{\sin }^{-1}}\left( \frac{2\lambda }{d} \right)\]

Given \[y=D\left( 2\,{{\theta }_{2}} \right)=8\times {{10}^{-2}}\]

Or \[1.5\times 2\times {{\sin }^{-1}}\left( \frac{2\lambda }{d} \right)=8\times {{10}^{-2}}\] \[\Rightarrow \]\[d\,\simeq \,0.005\operatorname{cm}\]