Tag: wave propagation (huygens' construction)

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

Indentify the correct statement from the following

  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.
Reveal answer Fill a bubble to check yourself
A,D Correct answer
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.

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

Huygen's concept of secondary wave

  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
Reveal answer Fill a bubble to check yourself
B Correct answer
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.

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

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:

  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 } } $
Reveal answer Fill a bubble to check yourself
B Correct answer
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.

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

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

  1. 90

  2. 81

  3. 67

  4. 72.85
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Maximum intensity I_max is proportional to (a1 + a2)^2 = 100 units, meaning a1 + a2 = 10. Reducing the width of one source by 50% reduces its amplitude by a factor of sqrt(0.5). Solving for the new amplitudes and calculating the new maximum intensity via (a1 + a_new)^2 yields approximately 72.85 units.

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

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

  1. $32m$
  2. $69 m$
  3. $16 m$
  4. $8 m$
Reveal answer Fill a bubble to check yourself
A Correct answer
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
$\therefore z _f=32m$.
Multiple choice physics wave optics huygens wave theory and wavefront wave propagation (huygens' construction) theories on light wave behaviour

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

  1. $\pi/8$
  2. $\pi/4$
  3. $\pi/2$
  4. $\pi$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

At the first minimum, the path difference between the edges of the slit is lambda. The path difference between the edge and the midpoint is lambda/2, which corresponds to a phase difference of pi.

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

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

  1. $10 sec$
  2. $1 sec$
  3. $10^{-3}$ sec
  4. $10^{-8}$ sec
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

In ordinary light sources, light is emitted due to independent atomic transitions lasting roughly 10^-8 seconds, during which the phase remains relatively constant before a sudden random phase change occurs.