Question

Two beams of light of intensity $ {{I}_{1}} $ and $ {{I}_{2}} $ interfere to give an interference pattern. If the ratio of maximum intensity to that of minimum intensity is $ \frac{25}{9} $ , then $ \frac{{{I}_{1}}}{{{I}_{2}}} $ is

• A. $ \frac{5}{3} $
• B. $ 4 $
• C. $ \frac{81}{625} $
• D. $ 16 $
• E. $ \frac{1}{2} $

Answer 1

Answer: (D)

$ \frac{{{I}_{\max }}}{{{I}_{\min }}}=\frac{25}{9} $ Or $ {{\left( \frac{{{a}_{1}}+{{a}_{2}}}{{{a}_{1}}-{{a}_{2}}} \right)}^{2}}=\frac{25}{9} $ where a denotes amplitude.
Or $ \frac{{{a}_{1}}+{{a}_{2}}}{{{a}_{1}}-{{a}_{2}}}=\frac{5}{3} $
Or $ \frac{{{a}_{1}}}{{{a}_{2}}}=4 $
As, $ {{(amplitude)}^{2}}\propto intensity $
Hence, $ \frac{{{I}_{1}}}{{{I}_{2}}}={{\left( \frac{{{a}_{1}}}{{{a}_{2}}} \right)}^{2}}=16 $