Optics Question 891
Question: When the diffraction pattern from a certain slit illuminated with laser light $ (\lambda =6330A^{o}) $ 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:
Options:
A) the slit is approximately 0.005 cm wide
B) the slit is approximately 0.05 cm wide
C) $ a/\lambda $ , is approximately 7.5 (a is the slit width)
D) $ a/\lambda $ is approximately 750
Show Answer
Answer:
Correct Answer: A
Solution:
[a] $ \sin {\theta _{2}}=\frac{2\lambda }{d} $
or $ {\theta _{2}}={{\sin }^{-1}}( \frac{2\lambda }{d} ) $
Given $ y=D(2{\theta _{2}})=8\times {{10}^{-2}} $
or $ 1.5\times 2\times {{\sin }^{-1}}( \frac{2\lambda }{d} )=8\times {{10}^{-2}} $
$ \Rightarrow d\simeq 0.005cm $
