Tag: wave propagation (huygens' construction)

Questions Related to wave propagation (huygens' construction)

Indentify the correct statement from the following

physics wave optics huygens wave theory and wavefront wave propagation (huygens' construction) theories on light wave behaviour

  1. Wave nature of light was proposed by Huygen.

  2. The direction of light ray and its wave front are opposite.

  3. Huygen's wave theory could not explain phenomenon of reflection.

  4. A monochromatic ray of light after passing through the prism should be made of one colour only.

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Correct Option: A,D
Explanation:

Huygen's wave theory: This wave theory was given by Huygens in 1678. According to this theory, a source of light propagates spherical waves in hypothetical.

In optics a ray is an idealized model of light, obtained by choosing a line that is perpendicular to the wavefronts of the actual light, and that points in the direction of energy flow.
Huygen’s wave theory could easily explain reflection, energy transmission, and refraction, but had difficulty explaining the straight line travel of light.
When a ray of monochromatic light would pass through a prism, you would see it refract but it will not disperse as its a beam of single wavelength. When light enters a medium with a different density it bends (refracts). Because white light contains a collection of component colors with varying wavelengths.

Huygen's concept of secondary wave

physics wave optics huygens wave theory and wavefront wave propagation (huygens' construction) theories on light wave behaviour

  1. allow up to find the focal length of a thick lens

  2. is a geometrical method to find a wavefront

  3. is used to determine the velocity of light

  4. is used to explain polarization

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Correct Option: B
Explanation:

Huygen proposed a hypothesis for the geometrical construction of the position of a common wavefront at any instant during the propagations of waves in a medium.

The wavefront of a lightbeam is given by the equation $x+2y+3z=c$,(where c is arbitary constant) the angle made by the direction of light with the y-axis is:

physics wave optics huygens wave theory and wavefront wave propagation (huygens' construction) theories on light wave behaviour

  1. ${ cos }^{ -1 }\frac { 1 }{ \sqrt { 14 } } $

  2. ${ cos }^{ -1 }\frac { 2 }{ \sqrt { 14 } } $

  3. ${ sin }^{ -1 }\frac { 1 }{ \sqrt { 14 } } $

  4. ${ sin }^{ -1 }\frac { 2 }{ \sqrt { 14 } } $

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Correct Option: B
Explanation:

Given,

Direction of light, $\vec n=\hat i+2\hat j+3\hat k$
The angle made by the direction of light with y-axis is
$cos\beta=\hat n.\hat j$
$cos\beta=\dfrac{\vec n}{|\vec n|}.\hat j$
$cos\beta=\dfrac{(\hat i+2\hat j+3\hat k).(0\hat i+\hat j+0\hat k)}{\sqrt{(1)^2+(2)^2+(3)^2}}=\dfrac{2}{\sqrt{14}}$
$\beta=cos^{-1}\dfrac{2}{\sqrt{14}}$
The correct option is B.

In which of the following cases do we obtain a plane wave front?

physics wave optics huygens wave theory and wavefront wave propagation (huygens' construction) theories on light wave behaviour

  1. Light emitted by a point source in an isotropic medium

  2. Light emerging from a convex lens when a point source is placed at its focus

  3. Light of the sun reaching the earth

  4. Light diverging from a slit.

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Correct Option: A

The two coherent sources of equal intensity produce maximum intensity of $100$ units at a point. If the intensity of one of the sources is reduced by $50\%$ by reducing its width then the intensity of light at the same point will be

physics wave optics huygens wave theory and wavefront wave propagation (huygens' construction) theories on light wave behaviour

  1. 90

  2. 81

  3. 67

  4. 72.85

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Correct Option: B

 For what distance ray optics a good approximation when the aperture is 4 mm wide and the wavelength is 500nm?

physics wave optics huygens wave theory and wavefront wave propagation (huygens' construction) theories on light wave behaviour

  1. $32m$

  2. $69 m$

  3. $16 m$

  4. $8 m$

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Correct Option: A
Explanation:
The Good approximation distance till ray optics or valid is given by Fresnel distance which is given by
$z _f=\dfrac{a^2}{\lambda}$
$z _f$ is distance till which diffraction effects of light can be neglected.
$a=$ aperature$=4\times 10^{-3}m$
$\lambda =$wavelength$=500\times 10^{-9}$m
$z _f=\dfrac{(4\times 10^{-3})^2}{(500\times 10^{-9})m}$
$=\dfrac{16\times 10^{-6}}{500\times 10^{-9}}$
$=0.032\times 10^3$m
$\therefore z _f=32m$.

A monochromatic light is incident on a single slit of width $24\times 10^{-5}\ cm$. Calculate wavelength of light if angular position of $1^{st}$ secondary maxima is $30^{o}$.

physics wave optics huygens wave theory and wavefront wave propagation (huygens' construction) theories on light wave behaviour

  1. $8000\ A^{o}$

  2. $12000\ A^{o}$

  3. $6000\ A^{o}$

  4. $16000\ A^{o}$

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Correct Option: C

At the first minimum adjacent to the central maximum of a single slit diffraction plate the phase difference between the huygens wavelet from the edge of the slit and the wavelet from the midpoint of the slate

physics wave optics huygens wave theory and wavefront wave propagation (huygens' construction) theories on light wave behaviour

  1. $\pi/8$

  2. $\pi/4$

  3. $\pi/2$

  4. $\pi$

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Correct Option: D

If light waves emitted by an ordinary source, for what period of time, the phase remains constant :-

physics wave optics huygens wave theory and wavefront wave propagation (huygens' construction) theories on light wave behaviour

  1. $10 sec$

  2. $1 sec$

  3. $10^{-3}$ sec

  4. $10^{-8}$ sec

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Correct Option: B

According to Huygen's theory of light

physics wave optics huygens wave theory and wavefront wave propagation (huygens' construction) theories on light wave behaviour

  1. light is stream of photon

  2. light is wave

  3. light behaves as particle

  4. None of the above

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Correct Option: B