Tag: wave optics

Questions Related to wave optics

Mark the CORRECT statements(s)

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

  1. Direction of wave propagation is along the normal to wavefront.

  2. For a point source of light, the shape of wavefront can be considered to be plane at very large

    distance from the source.

  3. A point source of light is placed at the focus of a thin spherical lens, then the shape of the wavefront for emerged light may be plane.

  4. The shape of the wavefront for the light incident on a thin spherical lens (kept in vacuum) is plane, the shape of the wavefront corresponding to emergent light would be always spherical.

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Correct Option: A,B,C,D
Explanation:

According to convention, direction of wave propagation is along the normal to wavefront.

The wavefront of a point source of light is spherical. A sphere with large radius is like a plane at its surface. Thus for a point source of light, the shape of wavefront can be considered to be plane at very large distance from the source.
Beam of light from a point source emerges parallel to principle axis when kept at focus of a thin spherical lens. Thus the wavefront emergent from the lens is planar.

A: The corpuscular theory fails in explaining the velocities of light in air and water.
B: According to corpuscular theory, the light should travel faster in a 'denser medium than in a rarer medium.

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

  1. If both A and B are true but the B is the correct explanation of A

  2. If both A and B are true but the B is not the correct explanation of A

  3. If A is true but B is false

  4. If both the A and B are false

  5. If B is true but A is false

Show answer
Correct Option: A
Explanation:

Corpuscular theory fails to explain the velocity of light in air and water because it predicted light to have more velocity in denser medium where as the fact is just the opposite. So option (a) is correct.

Corpuscular theory of light was advanced by

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

  1. Huygen

  2. Newton

  3. Maxwell

  4. Hertz

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Correct Option: B
Explanation:

$Answer:$ B

The corpuscular theory was largely developed by Sir Isaac newton. Newton's theory remained in force for more than 100 years and took precedence over Huygen's wave front theory, partly because of Newton’s great prestige. When the corpuscular theory failed to adequately explain the diffraction, interference and polarization of light it was abandoned in favour of Huygens' wave theory.

Wave front means:

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

  1. all particles in it have same phase

  2. few particles are in same phase, rest are in opposite phase

  3. all particles have opposite phase of vibrations

  4. all particles have random vibrations

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Correct Option: A
Explanation:

All particles in it have same phase.

It is the imaginary surface representing corresponding points pf a wave that vibrate in unison. When identical waves having a common origin travel through a homogeneous medium , the corresponding crests and troughs at any instant phase.

A wavefront is an imaginary surface where :

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

  1. phase is same for all points

  2. phase changes at constant rate at all points along the surface

  3. constant phase difference continuously changes between the points

  4. phase changes all over the surface

Show answer
Correct Option: A
Explanation:

A wave front is the locus of points having the same phase.
Hence option A is correct.

The shape of wave front at a very large distance from source is ______

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

  1. Circular

  2. Spherical

  3. Cylindrical

  4. Plane

Show answer
Correct Option: D
Explanation:

Due to the large distance, the radius of the wavefront can be considered as large (infinity) and hence, a wavefront is almost plane.

The wavefront of a light beam is given by the equation $x + 2 y + 3 z = c$ , (where c is arbitrary constant) then what is the angle made by the direction of light with the y-axis?

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

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

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

  3. $\cos ^ { - 3 } \frac { 2 } { \sqrt { 14 } }$

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

Show answer
Correct Option: B
Explanation:

The wave front equations must be of form $ax+by+cz=1$ where ${a^2} + {b^2} + {c^2} = 1$ 

$($ $a,b,c$ are cosines of angles made with $x,yx,z$ axes respectively $)$
applying this to the given equation$:$
${1^2} + {2^2} + {3^2} = {c^2}$
${c^2} = 14$
$c = \sqrt {14} $
${\cos ^{ - 1}}\dfrac{2}{{\sqrt {14} }}$
angle made with $y-$ axis is ${\cos ^{ - 1}}\dfrac{2}{{\sqrt {14} }}$
Hence,
option $(B)$ is correct answer. 

Light waves travel in a vacuum, along the $X-$axis. Which of the following may represent the wave fronts?

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

  1. $x=c$

  2. $y=c$

  3. $z=c$

  4. $x+y+z=c$

Show answer
Correct Option: A
Explanation:

Given the direction of propagation is $ \hat{i} $
Wave fronts will be planes $ \perp \hat{i} $
In the given options, only plane $ x=c $ is  $ \perp \hat{i} $

The wavefront is a surface in which

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

  1. all points are in the same phase

  2. there is a pair of points in opposite phase

  3. there is a pair of points with phase difference $(\dfrac{\pi}{2})$

  4. there is no relation between the phases

Show answer
Correct Option: A
Explanation:

A wavefront is the locus of points characterized by propagation of position of the same phase: a propagation of a line in 1D, a curve in 2D or a surface for a wave in 3D.

The wave front is a surface in which:

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

  1. All points are in the same phase

  2. There is a pair of points in opposite phase

  3. There is a pair of points with phase difference $(\cfrac {\pi}{2})$

  4. There is no relation between the phase

Show answer
Correct Option: A
Explanation:

 A wavefront is the locus of points having the same phase.