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In a Young’s double slit experiment, an angular width of the fringe is 0.53° on a screen place at 2m away for particular wavelength of 450 nm. The angular width of the fringe, when whole system is immersed in a medium of refractive index 7/5, is $\frac{1}{α} .$ The value of a is__________.

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Vishal Baghel | Contributor-Level 10

2 months ago

we know, = $\frac{λ}{d}$ $\frac{}{}$ $μ = \frac{C}{V} = \frac{C}{υ λ}$ $\frac{}{} \frac{}{}$

$_{} \frac{}{_{}_{}}$ $λ_{1} = \frac{C}{μ_{1} υ_{1}}$ [with change in medium frequency remain constant]

$λ_{2} = \frac{C}{μ_{2} υ_{2}}$

$\frac{λ_{2}}{λ_{1}} = \frac{μ_{1}}{μ_{2}} = \frac{5}{7}$ $λ_{2} = \frac{5}{7} λ_{1}$

$θ_{1} = \frac{λ_{1}}{d_{1}}$

2= $\frac{λ_{2}}{d_{2}}$

$\frac{θ_{2}}{θ_{1}} = \frac{λ_{2}}{λ_{1}} [? d_{1} = d_{2}]$

2 $= \frac{5}{7} \times θ_{1}$

$θ_{2} = \frac{5}{7} \times 0.35$

we know, = <math> <mrow> <mfrac> <mrow> <mi>λ</mi> </mrow> <mrow> <mi>d</mi> </mrow> </mfrac> </mrow> </math> <math><mrow><mfrac><mrow></mrow><mrow></mrow></mfrac></mrow></math> <math> <mrow> <mi>μ</mi> <mo>=</mo> <mfrac> <mrow> <mi>C</mi> </mrow> <mrow> <mi>V</mi> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mi>C</mi> </mrow> <mrow> <mi>υ</mi> <mi>λ</mi> </mrow> </mfrac> </mrow> </math> <math><mrow><mfrac><mrow></mrow><mrow></mrow></mfrac><mfrac><mrow></mrow><mrow></mrow></mfrac></mrow></math><math><mrow><msub><mrow></mrow><mrow></mrow></msub><mfrac><mrow></mrow><mrow><msub><mrow></mrow><mrow></mrow></msub><msub><mrow></mrow><mrow></mrow></msub></mrow></mfrac></mrow></math>  <math> <mrow> <msub> <mrow> <mi>λ</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <mi>C</mi> </mrow> <mrow> <msub> <mrow> <mi>μ</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <msub> <mrow> <mi>υ</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> </mrow> </mfrac> </mrow> </math> [with change in medium frequency remain constant] <math> <mrow> <msub> <mrow> <mi>λ</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <mi>C</mi> </mrow> <mrow> <msub> <mrow> <mi>μ</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> <msub> <mrow> <mi>υ</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> </mfrac> </mrow> </math> <math> <mrow> <mfrac> <mrow> <msub> <mrow> <mi>λ</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> <mrow> <msub> <mrow> <mi>λ</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <msub> <mrow> <mi>μ</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> </mrow> <mrow> <msub> <mrow> <mi>μ</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mn>5</mn> </mrow> <mrow> <mn>7</mn> </mrow> </mfrac> </mrow> </math> <math> <mrow> <msub> <mrow> <mi>λ</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <mn>5</mn> </mrow> <mrow> <mn>7</mn> </mrow> </mfrac> <msub> <mrow> <mi>λ</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> </mrow> </math> <math> <mrow> <msub> <mrow> <mi>θ</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <msub> <mrow> <mi>λ</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> </mrow> <mrow> <msub> <mrow> <mi>d</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> </mrow> </mfrac> </mrow> </math> 2= <math> <mrow> <mfrac> <mrow> <msub> <mrow> <mi>λ</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> <mrow> <msub> <mrow> <mi>d</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> </mfrac> </mrow> </math> <math> <mrow> <mfrac> <mrow> <msub> <mrow> <mi>θ</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> <mrow> <msub> <mrow> <mi>θ</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <msub> <mrow> <mi>λ</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> <mrow> <msub> <mrow> <mi>λ</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> </mrow> </mfrac> <mtext> </mtext> <mtext> </mtext> <mtext> </mtext> <mtext> </mtext> <mtext> </mtext> <mtext> </mtext> <mtext> </mtext> <mtext> </mtext> <mtext> </mtext> <mtext> </mtext> <mtext> </mtext> <mtext> </mtext> <mo stretchy="false">[</mo> <mo>?</mo> <msub> <mrow> <mi>d</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mo>=</mo> <msub> <mrow> <mi>d</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> <mo stretchy="false">]</mo> </mrow> </math> 2 <math> <mrow> <mo>=</mo> <mfrac> <mrow> <mn>5</mn> </mrow> <mrow> <mn>7</mn> </mrow> </mfrac> <mo>×</mo> <msub> <mrow> <mi>θ</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> </mrow> </math> <math> <mrow> <msub> <mrow> <mi>θ</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <mn>5</mn> </mrow> <mrow> <mn>7</mn> </mrow> </mfrac> <mo>×</mo> <mn>0</mn> <mo>.</mo> <mn>3</mn> <mn>5</mn> </mrow> </math>

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In a Young’s double slit experiment, an angular width of the fringe is 0.53° on a screen place at 2m away for particular wavelength of 450 nm. The angular width of the fringe, when whole system is immersed in a medium of refractive index 7/5, is $\frac{1}{α} .$ The value of a is__________.

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In a Young’s double slit experiment, an angular width of the fringe is 0.53° on a screen place at 2m away for particular wavelength of 450 nm. The angular width of the fringe, when whole system is immersed in a medium of refractive index 7/5, is 1 α . The value of a is__________.

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In a Young’s double slit experiment, an angular width of the fringe is 0.53° on a screen place at 2m away for particular wavelength of 450 nm. The angular width of the fringe, when whole system is immersed in a medium of refractive index 7/5, is $\frac{1}{α} .$ The value of a is__________.