Answer

Verified

340.2k+ views

**Hint:**In this question first we have to find intensity of light $\left( {{I}_{0}} \right)$ and phase difference $\left( \phi \right)$in first case central fringe intensity is given so by using intensity equation we can find intensity of light after that we can find phase difference $\phi $ using relation between phase difference and path difference by using this two values we can find the intensity at the given wavelength.

**Formula used:**

$I=4{{I}_{0}}{{\cos }^{2}}\dfrac{\phi }{2}$

And

$\phi =\dfrac{2\pi }{\lambda }\Delta x$

**Complete answer:**

It is given that intensity of central fringe on the screen

${{I}_{c}}=0.01W/{{m}^{2}}$

To find the intensity of fringe we will use below formula,

$I=4{{I}_{0}}{{\cos }^{2}}\dfrac{\phi }{2}......\left( 1 \right)$

Where, I = intensity of light after polarization

${{I}_{0}}$= original intensity of light

$\phi =$ Phase difference

To find the intensity of any path difference we will have to find the intensity of original light$\left( {{I}_{0}} \right)$.

Now in case of central fringe $I={{I}_{c}}$ and phase difference $\left( \phi \right)$will be zero now substitute this values in equation (1)

$\begin{align}

& \Rightarrow {{I}_{c}}=4{{I}_{0}}{{\cos }^{2}}\left( 0 \right) \\

& \Rightarrow 0.01=4{{I}_{0}}\left( \because {{\cos }^{2}}\left( 0 \right)=1 \right) \\

& \therefore {{I}_{0}}=\dfrac{0.01}{4}....\left( 2 \right) \\

\end{align}$

Now in order to find the phase difference we will use relation between phase difference and path difference

$\phi =\dfrac{2\pi }{\lambda }\Delta x......\left( 3 \right)$

$\Delta x$ = path difference

$\lambda =$ Wavelength

Value of path difference is given

$\Delta x=\dfrac{\lambda }{3}.....\left( 4 \right)$

Now put values of $\Delta x$ in equation (3)

$\begin{align}

& \Rightarrow \phi =\dfrac{2\pi }{\lambda }\times \dfrac{\lambda }{3} \\

& \therefore \phi =\dfrac{2\pi }{3}.....\left( 5 \right) \\

\end{align}$

Now we will put value of equation (2) and equation (5) in equation (1)

$\begin{align}

& \Rightarrow I=4{{I}_{0}}{{\cos }^{2}}\dfrac{\phi }{2} \\

& \Rightarrow I=4\times \dfrac{0.01}{4}\times {{\cos }^{2}}\left( \dfrac{2\pi }{3\times 2} \right) \\

& \Rightarrow I=0.01\times {{\cos }^{2}}\left( \dfrac{\pi }{3} \right) \\

& \Rightarrow I=0.01\times {{\left( \dfrac{1}{2} \right)}^{2}} \\

& \Rightarrow I=\dfrac{0.01}{4} \\

& \therefore I=0.0025W/{{m}^{2}} \\

\end{align}$

We have to convert in $mW/{{m}^{2}}$ so we have to multiply by 1000 now

$\begin{align}

& \Rightarrow I=0.0025\times 1000 \\

& \therefore I=2.5mW/{{m}^{2}} \\

\end{align}$

**So the correct option is (A) .**

**Note:**

Intensity of light in a particular direction per unit solid angle can be defined as the measure of the wavelength-weighted power emitted by a light source. Additionally, when we put value of ${{\cos }^{2}}\left( \dfrac{\pi }{3} \right)$ we have to remember at square sometimes we can do mistakes by putting values of ${{\cos }^{2}}\left( \dfrac{\pi }{3} \right)=\left( \dfrac{1}{2} \right)$ instead of${{\left( \dfrac{1}{2} \right)}^{2}}$ .

Recently Updated Pages

Basicity of sulphurous acid and sulphuric acid are

Three beakers labelled as A B and C each containing 25 mL of water were taken A small amount of NaOH anhydrous CuSO4 and NaCl were added to the beakers A B and C respectively It was observed that there was an increase in the temperature of the solutions contained in beakers A and B whereas in case of beaker C the temperature of the solution falls Which one of the following statements isarecorrect i In beakers A and B exothermic process has occurred ii In beakers A and B endothermic process has occurred iii In beaker C exothermic process has occurred iv In beaker C endothermic process has occurred

What is the stopping potential when the metal with class 12 physics JEE_Main

The momentum of a photon is 2 times 10 16gm cmsec Its class 12 physics JEE_Main

How do you arrange NH4 + BF3 H2O C2H2 in increasing class 11 chemistry CBSE

Is H mCT and q mCT the same thing If so which is more class 11 chemistry CBSE

Trending doubts

How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Describe the poetic devices used in the poem Aunt Jennifers class 12 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Difference Between Plant Cell and Animal Cell

Change the following sentences into negative and interrogative class 10 english CBSE

State the laws of reflection of light

State and prove Bernoullis theorem class 11 physics CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE