Ask Questions, Get Answers

Want to ask us a question? Click here
Browse Questions
Home  >>  JEEMAIN and AIPMT  >>  Physics  >>  Class12  >>  Wave Optics
0 votes

In a modified YDSE a monochromatic uniform and parallel beam of light of wavelength 6000 A and intensity $\bigg(\large\frac{10}{\pi}\bigg) \large\frac{w}{m^2}$ is incident normally on two circular operates A and B of radii $0.001\;m $ and $0.002\;m$ respectively. A perfectly transparent film of thickness $2000 A^{\circ}$ and refractive index $1.5 $ for wavelength $6000\;A^{\circ}$ is placed in front of aperture A. Calculate the pour (in waters) received at Focal spot F of lens. The lens is symmetrically placed with respect to aperture. Assume $10 \%$ of power received by each aperture goes in original direction and is bought to focal speet.

$(a)\;7 \times 10^{-4}\;watt \\ (b)\;7 \times 10^{-2} watt \\ (c)\;7 \times 10^{-6} watt \\ (d)\;7 \times 10^{-8} watt $

Can you answer this question?

1 Answer

0 votes
 $ P=IS$ , where A is the surface area
So Power received at A and B is respectively.
$P_A=\large\frac{10}{\pi}$$ \times \pi (0.001)^2 =10^{-5}w$
and $P_B=\large\frac{10}{\pi} $$\times \pi (0.002)^2= 4 \times 10^{-5}w$
and as only 10 % of incident power passes,
$P_A'= \large\frac{10}{100} $$\times 10^{-5}=10^{-6} w$
and $P_B'= \large\frac{10}{100} $$ 4 \times 10^{5}= 4 \times 10^{-6}w$
Now as due to introduction of film the path difference produced .
$\Delta x =(\mu-1) t $
$\qquad=(1.5-1) \times 2000=1000 A^{\circ}$
So, $ \phi =\large\frac{2 \pi}{\lambda} (\Delta x)= \large\frac{2\pi}{6000} $$ \times 1000 =\large\frac{n}{3}$
But as in interference,
$I=I_1+I_2+ 2 \sqrt {I_1 I_2} \cos \phi$
and if s is area of focal spot,
$P= IS= I_AS+I_BS+ 2S(\sqrt {I_A+I_B}) \cos \phi$
ie $P= PA'+PB'+2 \sqrt {PA'P_B'} \cos (\large\frac{\pi}{3})$
$P= 10^{-6} [1+4+2 \sqrt {1 \times 4}) \times (\frac{1}{2})]$
$\qquad= 7 \times 10^{-6}\;watt$
Hence c is the correct answer.
answered Feb 13, 2014 by meena.p
edited Jul 28, 2014 by meena.p

Related questions

Ask Question
student study plans
JEE MAIN, CBSE, NEET Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App