Optics Question 166
A circular disc is placed in front of a narrow source. When the point of observation is 2 m from the disc, then it covers first Huygens’ Zone. The intensity at this point is I. When the point of observation is 25 cm from the disc then intensity will be
Options:
A) $ {{( \frac{R _{6}}{R _{2}} )}^{2}}I $
B) $ {{( \frac{R _{7}}{R _{2}} )}^{2}}I $
C) $ {{( \frac{R _{8}}{R _{2}} )}^{2}}I $
D) $ {{( \frac{R _{9}}{R _{2}} )}^{2}}I $
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Answer:
Correct Answer: D
Solution:
$ I=\frac{R _{2}^{2}}{4} $ given $ n _{1}b _{1}=n _{2}b _{2} $
Therefore $ 1\times 200=n _{2}\times 25 $
$ \therefore n _{2}=8\ \text{Hz} $
$ \therefore I={{( \frac{R _{9}}{2} )}^{2}} $
$ ={{( \frac{R _{9}}{R _{8}}\times \frac{R _{8}}{R _{7}}\times \frac{R _{7}}{R _{6}}\times \frac{R _{6}}{R _{5}}\times \frac{R _{5}}{R _{4}}\times \frac{R _{4}}{R _{3}}\times \frac{R _{3}}{R _{2}}\times \frac{R _{2}}{R _{2}} )}^{2}} $
$ ={{( \frac{R _{9}}{R _{2}} )}^{2}}I $
BETA
