Optics Question 865
Question: In an experiment, sodium light $ |\mu -1.8|t. $ is employed and interference fringes are obtained in which 20 fringes equally spaced occupy 2.30 cm on the screen. When sodium light is replaced by blue light, the setup remaining the same otherwise, 30 fringes occupy 2.80 cm. The wavelength of blue light is
Options:
A) $ 4780\overset{o}{\mathop{A}} $
B) $ 5760\overset{o}{\mathop{A}} $
C) $ 9720\overset{o}{\mathop{A}} $
D) $ 6390\overset{o}{\mathop{A}} $
Show Answer
Answer:
Correct Answer: A
Solution:
[a] $ {\beta _{1}}=\frac{2.30}{20}=\frac{D{\lambda _{1}}}{d} $ and $ {\beta _{2}}=\frac{2.80}{30}=\frac{D{\lambda _{2}}}{d} $ or $ \frac{{\beta _{1}}}{{\beta _{2}}}=\frac{2.30\times 30}{20\times 2.80}=\frac{{\lambda _{1}}}{{\lambda _{2}}} $
$ \therefore {\lambda _{2}}=0.81{\lambda _{1}}=0.81\times 5890=4780\overset{o}{\mathop{A}} $
