Visible light of wavelength <math> <mn>6000</mn> <mo>×</mo> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mo>-</mo> <mn>8</mn> </mrow> </mrow> </msup> <mtext> </mtext> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">m</mi> </math> <math><msup><mrow><mrow></mrow></mrow><mrow><mrow></mrow></mrow></msup><mtext></mtext></math> falls normally on a single slit and produces a diffraction pattern. It is found that the second diffraction minimum is at <math> <msup> <mrow> <mrow> <mn>60</mn> </mrow> </mrow> <mrow> <mrow> <mo>?</mo> </mrow> </mrow> </msup> </math> <math><msup><mrow><mrow></mrow></mrow><mrow><mrow></mrow></mrow></msup></math> from the central maximum. If the first minimum is produced at <math> <msub> <mrow> <mrow> <mi>θ</mi> </mrow> </mrow> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> </msub> </math> <math><msub><mrow><mrow></mrow></mrow><mrow><mrow></mrow></mrow></msub></math> then <math> <msub> <mrow> <mrow> <mi>θ</mi> </mrow> </mrow> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> </msub> </math> <math><msub><mrow><mrow></mrow></mrow><mrow><mrow></mrow></mrow></msub></math> is close to:

For 2 nd minima d s i n ? θ = 2 λ s i n ? θ = 3 2 (given) ⇒ λ d = 3 4 So for 1 st minima is d s i n ? θ = λ s i n ? θ = λ d = 3 4 (from equation (i) θ = 25.65 ? (from sin table) θ ≈ 25 ? .

Visible light of wavelength <math> <mn>6000</mn> <mo>×</mo> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mo>-</mo> <mn>8</mn> </mrow> </mrow> </msup> <mtext> </mtext> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">m</mi> </math> <math><msup><mrow><mrow></mrow></mrow><mrow><mrow></mrow></mrow></msup><mtext></mtext></math>&nbsp;falls normally on a single slit and produces a diffraction pattern. It is found that the second diffraction minimum is at <math> <msup> <mrow> <mrow> <mn>60</mn> </mrow> </mrow> <mrow> <mrow> <mo>?</mo> </mrow> </mrow> </msup> </math> <math><msup><mrow><mrow></mrow></mrow><mrow><mrow></mrow></mrow></msup></math>&nbsp;from the central maximum. If the first minimum is produced at <math> <msub> <mrow> <mrow> <mi>θ</mi> </mrow> </mrow> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> </msub> </math> <math><msub><mrow><mrow></mrow></mrow><mrow><mrow></mrow></mrow></msub></math>&nbsp;then <math> <msub> <mrow> <mrow> <mi>θ</mi> </mrow> </mrow> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> </msub> </math> <math><msub><mrow><mrow></mrow></mrow><mrow><mrow></mrow></mrow></msub></math>&nbsp;is close to:

Ask & Answer Question

Physics Class 12th Physics Wave Optics

Visible light of wavelength $6000 \times 10^{- 8} c m$ $^{}$ falls normally on a single slit and produces a diffraction pattern. It is found that the second diffraction minimum is at $60^{?}$ $^{}$ from the central maximum. If the first minimum is produced at $θ_{1}$ $_{}$ then $θ_{1}$ $_{}$ is close to:

Option 1 -

$20^{\circ}$

Option 2 -

$30^{\circ}$

Option 3 -

$25^{\circ}$

Option 4 -

$45^{\circ}$

2 Views | Posted 2 months ago

Asked by Shiksha User

1 Answer

Answered by

Vishal Baghel | Contributor-Level 10

2 months ago

Correct Option - 3

Detailed Solution:

For $2^{nd}$ $^{}$ minima

$d s i n ? θ = 2 λ$

$s i n ? θ = \frac{\sqrt[]{3}}{2}$ (given)

$\Rightarrow \frac{λ}{d} = \frac{\sqrt[]{3}}{4}$

So for $1^{st}$ $^{}$ minima is

$d s i n ? θ = λ$

$s i n ? θ = \frac{λ}{d} = \frac{\sqrt[]{3}}{4}$ (from equation (i)

$θ = {25.65}^{?}$ (from sin table)

$^{}$ $θ \approx 25^{?}$ .

For <math> <msup> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> <mrow> <mrow> <mtext>nd</mtext> <mtext> </mtext> </mrow> </mrow> </msup> </math> <math><msup><mrow><mrow></mrow></mrow><mrow><mrow></mrow></mrow></msup></math> minima <math> <mi mathvariant="normal">d</mi> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">n</mi> <mo>? </mo> <mi>θ</mi> <mo>=</mo> <mn>2</mn> <mi>λ</mi> </math> <math><mfrac><mrow><mrow><mroot><mrow><mrow></mrow></mrow></mroot></mrow></mrow></mfrac></math> <math> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">n</mi> <mo>? </mo> <mi>θ</mi> <mo>=</mo> <mfrac> <mrow> <mrow> <mroot> <mrow> <mrow> <mn>3</mn> </mrow> </mrow> <mrow></mrow> </mroot> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </mfrac> </math>   (given) <math> <mo>⇒</mo> <mrow> <mi mathvariant="normal"> </mi> </mrow> <mfrac> <mrow> <mrow> <mi>λ</mi> </mrow> </mrow> <mrow> <mrow> <mi mathvariant="normal">d</mi> </mrow> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mrow> <mroot> <mrow> <mrow> <mn>3</mn> </mrow> </mrow> <mrow></mrow> </mroot> </mrow> </mrow> <mrow> <mrow> <mn>4</mn> </mrow> </mrow> </mfrac> </math> So for <math> <msup> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> <mrow> <mrow> <mtext>st</mtext> <mtext> </mtext> </mrow> </mrow> </msup> </math> <math><msup><mrow><mrow></mrow></mrow><mrow><mrow></mrow></mrow></msup></math> minima is <math> <mi mathvariant="normal">d</mi> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">n</mi> <mo>? </mo> <mi>θ</mi> <mo>=</mo> <mi>λ</mi> </math> <math><mfrac><mrow><mrow></mrow></mrow></mfrac></math> <math> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">n</mi> <mo>? </mo> <mi>θ</mi> <mo>=</mo> <mfrac> <mrow> <mrow> <mi>λ</mi> </mrow> </mrow> <mrow> <mrow> <mi>d</mi> </mrow> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mrow> <mroot> <mrow> <mrow> <mn>3</mn> </mrow> </mrow> <mrow></mrow> </mroot> </mrow> </mrow> <mrow> <mrow> <mn>4</mn> </mrow> </mrow> </mfrac> </math>   (from equation (i)<math></math> <math> <mi>θ</mi> <mo>=</mo> <msup> <mrow> <mrow> <mn>25.65</mn> </mrow> </mrow> <mrow> <mrow> <mo>? </mo> </mrow> </mrow> </msup> <mrow> <mi mathvariant="normal"> </mi> </mrow> </math>   (from sin table)<math><msup><mrow><mrow></mrow></mrow><mrow><mrow></mrow></mrow></msup></math>  <math> <mi>θ</mi> <mo>≈</mo> <msup> <mrow> <mrow> <mn>25</mn> </mrow> </mrow> <mrow> <mrow> <mo>? </mo> </mrow> </mrow> </msup> </math> .

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Visible light of wavelength 6000 × 10 - 8 c m falls normally on a single slit and produces a diffraction pattern. It is found that the second diffraction minimum is at 60 ? from the central maximum. If the first minimum is produced at θ 1 then θ 1 is close to: