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Physics Ncert Solutions Class 12th Physics Class 12th Wave Optics

10.7 In a double-slit experiment the angular width of a fringe is found to be 0.2° on a screen placed 1 m away. The wavelength of light used is 600 nm. What will be the angular width of the fringe if the entire experimental apparatus is immersed in water? Take refractive index of water to be 4/3.

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Payal Gupta | Contributor-Level 10

5 months ago

10.7 Distance of the screen from the slits, D = 1 m

Wavelength of the light used, $?_{1}$ = 600 nm

Angular width of the fringe in air, $?_{1}$ = 0.2 $°$

Angular width of the fringe in water = $?_{2}$

Refractive index of water, $? = \frac{4}{3}$

Refractive index is related to angular width as:

$? = \frac{?_{1}}{?_{2}}$ or

$?_{2} = \frac{?_{1}}{?}$ = 0.2 $* \frac{3}{4}$ = 0.15 $°$

Hence, the angular width of the fringes in water will be 0.15 $°$

10.7 Distance of the screen from the slits, D = 1 mWavelength of the light used,  <math><msub><mrow><mrow><mi>? </mi></mrow></mrow><mrow><mrow><mn>1</mn></mrow></mrow></msub></math> = 600 nmAngular width of the fringe in air,  <math><msub><mrow><mrow><mi>? </mi></mrow></mrow><mrow><mrow><mn>1</mn></mrow></mrow></msub></math> = 0.2 <math><mo>°</mo></math>Angular width of the fringe in water = <math><msub><mrow><mrow><mi>? </mi></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></msub></math>Refractive index of water,  <math><mi>? </mi><mo>=</mo><mfrac><mrow><mrow><mn>4</mn></mrow></mrow><mrow><mrow><mn>3</mn></mrow></mrow></mfrac></math>Refractive index is related to angular width as:<math><mi>? </mi><mo>=</mo><mi></mi><mfrac><mrow><mrow><msub><mrow><mrow><mi>? </mi></mrow></mrow><mrow><mrow><mn>1</mn></mrow></mrow></msub></mrow></mrow><mrow><mrow><msub><mrow><mrow><mi>? </mi></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></msub></mrow></mrow></mfrac></math> or<math><msub><mrow><mrow><mi>? </mi></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></msub><mo>=</mo><mi></mi><mfrac><mrow><mrow><msub><mrow><mrow><mi>? </mi></mrow></mrow><mrow><mrow><mn>1</mn></mrow></mrow></msub></mrow></mrow><mrow><mrow><mi>? </mi></mrow></mrow></mfrac></math> = 0.2 <math><mo>*</mo><mfrac><mrow><mrow><mn>3</mn></mrow></mrow><mrow><mrow><mn>4</mn></mrow></mrow></mfrac></math> = 0.15 <math><mo>°</mo></math>Hence, the angular width of the fringes in water will be 0.15 <math><mo>°</mo></math>

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10.7 In a double-slit experiment the angular width of a fringe is found to be 0.2° on a screen placed 1 m away. The wavelength of light used is 600 nm. What will be the angular width of the fringe if the entire experimental apparatus is immersed in water? Take refractive index of water to be 4/3.

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