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Sodium light of wavelength 650nm and 655 nm is used to study diffraction at a single slit of aperture 0.5 mm. The distance between the slit and the screen is 2.0 m. The separation between the positions of the first maximum of diffraction pattern obtained in the two cases is _________× 10^-⁵ m.

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alok kumar singh | Contributor-Level 10

a month ago

For maxima = y = (2n + 1) $\frac{λ}{2} \frac{D}{a}$

For 1^st maxima for l₁ wavelength (n = 1)

$y_{1} = \frac{3 λ_{1}}{2} \frac{D}{a}$ - (1)

First maxima for l₂ wavelength

$y_{2} = \frac{3}{2} λ_{2} \frac{D}{a}$ - (2)

$\Rightarrow y_{2} - y_{1} = \frac{3}{2} \frac{D}{a} [λ_{2} - λ_{1}]$

$= \frac{3}{2} \times \frac{2 \times 5 \times 1 0^{- 9}}{0.5 \times 1 0^{- 3}}$

$= \frac{3}{1 0^{- 3}} \times 1 0^{- 8}$

For maxima = y = (2n + 1) <math> <mrow> <mfrac> <mrow> <mi>λ</mi> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> <mfrac> <mrow> <mi>D</mi> </mrow> <mrow> <mi>a</mi> </mrow> </mfrac> </mrow> </math> <!- [endif]-><!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1025" DrawAspect="Content" ObjectID="_1819202770"> </o:OLEObject></xml><! [endif]->For 1st maxima for l1 wavelength (n = 1) <math> <mrow> <msub> <mrow> <mi>y</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <mn>3</mn> <msub> <mrow> <mi>λ</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> <mfrac> <mrow> <mi>D</mi> </mrow> <mrow> <mi>a</mi> </mrow> </mfrac> </mrow> </math>          - (1)First maxima for l2 wavelength <math> <mrow> <msub> <mrow> <mi>y</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <mn>3</mn> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> <msub> <mrow> <mi>λ</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> <mfrac> <mrow> <mi>D</mi> </mrow> <mrow> <mi>a</mi> </mrow> </mfrac> </mrow> </math>          - (2) <math> <mrow> <mo>⇒</mo> <msub> <mrow> <mi>y</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> <mo>−</mo> <msub> <mrow> <mi>y</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <mn>3</mn> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> <mfrac> <mrow> <mi>D</mi> </mrow> <mrow> <mi>a</mi> </mrow> </mfrac> <mrow> <mo> [</mo> <mrow> <msub> <mrow> <mi>λ</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> <mo>−</mo> <msub> <mrow> <mi>λ</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> </mrow> <mo>]</mo> </mrow> </mrow> </math> <math> <mrow> <mo>=</mo> <mfrac> <mrow> <mn>3</mn> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> <mo>×</mo> <mfrac> <mrow> <mn>2</mn> <mo>×</mo> <mn>5</mn> <mo>×</mo> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mo>−</mo> <mn>9</mn> </mrow> </msup> </mrow> <mrow> <mn>0</mn> <mo>.</mo> <mn>5</mn> <mo>×</mo> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mo>−</mo> <mn>3</mn> </mrow> </msup> </mrow> </mfrac> </mrow> </math> <math> <mrow> <mo>=</mo> <mfrac> <mrow> <mn>3</mn> </mrow> <mrow> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mo>−</mo> <mn>3</mn> </mrow> </msup> </mrow> </mfrac> <mo>×</mo> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mo>−</mo> <mn>8</mn> </mrow> </msup> </mrow> </math>

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Sodium light of wavelength 650nm and 655 nm is used to study diffraction at a single slit of aperture 0.5 mm. The distance between the slit and the screen is 2.0 m. The separation between the positions of the first maximum of diffraction pattern obtained in the two cases is _________× 10^-⁵ m.

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Sodium light of wavelength 650nm and 655 nm is used to study diffraction at a single slit of aperture 0.5 mm. The distance between the slit and the screen is 2.0 m. The separation between the positions of the first maximum of diffraction pattern obtained in the two cases is _________× 10-5 m.

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Sodium light of wavelength 650nm and 655 nm is used to study diffraction at a single slit of aperture 0.5 mm. The distance between the slit and the screen is 2.0 m. The separation between the positions of the first maximum of diffraction pattern obtained in the two cases is _________× 10^-⁵ m.