In young’s double slit experiment performed using a monochromatic light of wavelength $\lambda ,$ when a glass plate $\left(\mu =1.5\right)$ of thickness $x\lambda$ is introduced in the path of the one of the interfering beams, the intensity at the position where the central maximum occurred previously remains unchanged. The value of x will be:

Correct Option - 2


Detailed Solution:

Þ AC = d + t   $\left(\mu -1\right)\to$ path length                       

BC = d

path different = AC – BC =  $n\lambda$

$t\left(\mu -1\right)=\mu \lambda$

for contal maxima

$x\lambda \left(1.5-1\right)=n\lambda$

Þ   

0.5x = x

n = 0, 1,2- -

n = 0  Not possible

Now, n = 1

0.5x = 1

x = 2

 

<p>Þ AC = d + t &lt;!- [if gte mso 9]>&lt;xml&gt; <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1025" DrawAspect="Content" ObjectID="_1814364447"> </o:OLEObject>&lt;/xml&gt;&lt;! [endif]-&gt;&nbsp;<span contenteditable="false"> <math> <mrow> <mrow> <mo> (</mo> <mrow> <mi>μ</mi> <mo>−</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> <mo>→</mo> </mrow> </math> </span>path length&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</p><p>BC = d</p><p>path different = AC – BC =&nbsp;&lt;!- [if gte mso 9]>&lt;xml&gt; <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1026" DrawAspect="Content" ObjectID="_1814364448"> </o:OLEObject>&lt;/xml&gt;&lt;! [endif]-&gt; <span contenteditable="false"> <math> <mrow> <mi>n</mi> <mi>λ</mi> </mrow> </math> </span></p><p><span contenteditable="false"> <math> <mrow> <mi>t</mi> <mrow> <mo> (</mo> <mrow> <mi>μ</mi> <mo>−</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mi>μ</mi> <mi>λ</mi> </mrow> </math> </span></p><p>for contal maxima</p><p><span contenteditable="false"> <math> <mrow> <mi>x</mi> <mi>λ</mi> <mrow> <mo> (</mo> <mrow> <mn>1</mn> <mo>.</mo> <mn>5</mn> <mo>−</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mi>n</mi> <mi>λ</mi> </mrow> </math> </span></p><p>Þ&nbsp;&lt;!- [if gte mso 9]>&lt;xml&gt; <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1028" DrawAspect="Content" ObjectID="_1814364450"> </o:OLEObject>&lt;/xml&gt;&lt;! [endif]-&gt;&nbsp;</p><p>0.5x = x</p><p>n = 0, 1,2- -</p><p>n = 0&nbsp; Not possible</p><p>Now, n = 1</p><p>0.5x = 1</p><p>x = 2</p><div class="photo-widget-full"><div class="figure"><picture><source srcset="" media=" (max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/1752838620phpJAD7kB.jpeg" alt="" width="412" height="373" loading="lazy"></picture></div></div><p>&nbsp;</p>

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