3 Marks Question

Question 13 Marks

Write Huygen's principle and explain how a new spherical wave front is formed after a very small time interval.

Answer

• Huygen's principle :
"Every point or particle of a wavefront behaves as an independent secondary source, emits by itself secondary spherical waves. After a very small time interval the surface tangential to all such secondary spherical wavelets gives the position and shape of the new wavefront."
→[Alternatively, "Each point of the wavefront is the source of a secondary disturbance and the wavelets emanating from these points spread out in all directions with the speed of the wave. These wavelets emanating from the wavefront are usually referred to as secondary wavelets and if we draw a common tangent to all these spheres, we obtain the new position of the wave front at a later time."]

→As shown in the Fig, $F _1 F_2$ represents the spherical wave front (with O as Centre) at $t=0$.
→As per Huygen's principle each point on the wavefront behaves as a secondary source and the waves emanating from these point spread equally in all directions at the speed of wave. If we wish to determine the shape of the wave front at $t=\tau$, we draw spheres of radius $v \tau$ from each point on the spherical wave front where $v$ represents the speed of the waves in the medium.
→If we now draw a common tangent to all these spheres, we obtain the new position of the wave front at $t =\tau$.
→The new wavefront is shown in the Fig. as $G _1 G _2$, which is again a spherical with point ' O ' as centre.

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Question 23 Marks

Explain the refraction of a plane wave by
(a) a thin prism
(b) a convex lens and
(c) reflection of a plane wave by a concave mirror.

Answer

(a) Refraction of a plane wave by a thin prism :

→Consider a plane wave passing through a thin prism.
→Since the speed of light wave is less in glass, lower portion of the incoming wavefront (which travels through the greatest thickness of the glass) will get delayed resulting in a tilt in the emerging wavefront as shown in the fig. (a).
(b) Refraction of a plane wave by a convex lens :

→As shown in fig. (b), a plane wave front is incident on a thin convex lens.
→The central part of the incident plane wave traverses the thickest portion of the lens and is delayed the most.
→The emerging wave front has a depression at the centre and therefore the wave front becomes spherical and converges to point $F$ which is known as the focus.
(c) Reflection of a plane wave front by a concave mirror :

→As shown in fig. (c), a plane wave is incident on a concave mirror and on reflection, we have a spherical wave converging to the focal point F .
→In a similar manner, we can understand reflection and refraction by concave lenses and convex mirrors.

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Question 33 Marks

Give explanation about wave front.
###
Explain Wave front.

Answer

→When we drop a small stone on a calm pool of water, waves spread out from the point of impact. Every point on the surface starts oscillating with time.
→At any instant the photograph of the surface would show circular rings, on which the disturbance is maximum. Clearly, all points on such a circle are oscillating in phase, because they are at the same distance from the source.
→Such a locus of points, which oscillate in phase is called a wave front.
→Thus, a wave front is defined as a surface of constant phase.
[In other words, "an imaginary surface passing through all the points oscillating in phase is called a wave front."
→The speed with which the wave front moves outwards from the source is called the speed of the wave. The energy of the wave travels in a direction perpendicular to the wave front.

→If we have a point source emitting waves uniformly in all directions, then the locus of points which have the same amplitude and vibrate in the same phase are spheres, and we will have what is known as a spherical wave as shown in fig. (a).
→At a large distance from the source, a small portion of the sphere can be considered as a plane, and we will have what is known as a plane wave. [fig.(b)]

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Question 43 Marks

Write and explain the super position principle (of waves).

Answer

• Super Position Principle :
"At a particular point in the medium, the resultant displacement produced by a number of waves is the vector sum of the displacements produced by each of the waves."

→As shown in fig. (a), two waves are moving towards each other on a string.
→Suppose, the maximum displacement of the particle under the effect of first wave is 0.5 cm and in the second wave, the maximum displacement is 0.3 cm .
→Here, both the waves are moving towards each other.
→As the two waves are approaching each other, at any instant both the waves will overlap in some region of the string. Then they move with their original shape and in their original direction.
→The net maximum displacement of the particle of string in overlapped region would be 0.5 cm $+0.3 cm=0.8 cm$
→Suppose, two persons snap the end of the string such that wave pulse generates at both the ends of the string as shown in fig. (b). In the first wave pulse the maximum displacement of the particle is 0.5 cm in upward and in the other wave pulse the maximum displacement of the particle is 0.5 cm in the downward direction.
→When the wave pulses approach each other, at some instant, they overlay on the string and displacement of all the particles will be 0.5 cm $+(-0.5 cm)=0$.
→Here, the velocities of the particles will not be zero.
→In this situation, string becomes stright everywhere, then both the wave pulses will emerge and move in their original direction.

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