question_answer

A ray of light of intensity I is incident on a parallel glass slab at a point A as shown in fig. It undergoes partial reflection and refraction. AT each reflection \[25%\] of incident energy is reflected. The rays AB and A?B? undergo interference. The ratio \[{{I}_{max}}/{{I}_{min}}\] is-

A) 4 : 1                 

B) 8 : 1

C) 7 : 1                             

D) 49 : 1

Correct Answer: D

Solution :

From figure \[{{I}_{1}}=\frac{I}{4}\] and \[{{I}_{2}}=\frac{9I}{64}\] \[\Rightarrow \,\,\,\frac{{{I}_{2}}}{{{I}_{1}}}\,\,=\,\,\frac{9}{16}\]         64 By using \[\frac{{{\operatorname{I}}_{max}}}{{{\operatorname{I}}_{min}}}\,\,\,=\,\,\,{{\left( \frac{\sqrt{\frac{{{I}_{2}}}{{{I}_{1}}}}+1}{\sqrt{\frac{{{I}_{2}}}{{{I}_{1}}}}-1} \right)}^{2}}\,\,=\,\,\,{{\left( \frac{\sqrt{\frac{9}{16}}+1}{\sqrt{\frac{9}{16}}-1} \right)}^{2}}\,\,=\,\,\frac{49}{1}\]