Physics Important Questions: Wave Theory of Light

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Q1. In the air, three media water, turpentine, and glass are separated by parallel plane boundaries. They have refractive indices μw, μt and μg with respect to air. What is the refractive index of glass with respect to turpentine?

Refractive index of water w.r.t. air

aμw = va/vw    …………… (1)

Refractive index of terpentine w.r.t. air

aμt = va/vt    …………… (2)

Refractive index of glass w.r.t. air

aμg = va/vg  …………… (3)

Refractive index of glass w.r.t. terpentine

tμg = vt/v= (va/vg)/(va/vt   …………… (4)

Substituting values of equation (2) and (3) in (4)

tμg  = (aμg)/(aμt)

∴  tμg  μg/μt

Q2. How does the wave normals travel in (a) plane wavefront (b) spherical wavefront?

• In a plane wavefront wave normal travels in a direction parallel to the direction of propagation of the wavefront.
• In a spherical wavefront, the wave normal travels in radially outward direction away from the source.

Q3. What is the angle of incidence when a ray of light passes from vacuum into a medium of a refractive index μ if the angle of incidence ‘i’ is found to be twice the angle of refraction ‘r’?

By snell’s law

Q3. A ray of light is incident on a medium at an angle ‘i’. It is found that the reflected ray and refracted ray are perpendicular. What is the refractive index of the medium?

• As the reflected ray and refracted ray are perpendicular to each other the incident angle must be the polarising angle.
• Hence by Brewster’s law, the refractive index of the medium is given by

μ = tan ip = tan i

Q4. Why polaroid glass is used in sunglasses?

• Light usually scatters in all directions; but when it’s reflected from flat surfaces, it tends to become polarized. This creates an annoying and sometimes dangerous intensity of reflected light that causes glare and reduces visibility.
• Polaroids are used in sunglasses to cut off the glare reflected by horizontal surfaces.

Q1. Define wavefront and wave normal.

• Wavefront: A wavefront is defined as the locus of all the points of a medium, which receives light wave disturbance simultaneously so that all these points are, in the same phase.
• Wave Normal: A perpendicular drawn to the surface of a wavefront at any point in the direction of propagation of light is called as Wave Normal.

Q2. Draw a neat labelled diagram of a) Spherical wavefront with wave normal. b) Plane wavefront with wave normal

• Spherical wavefront with wave normal:
• Plane wavefront with wave normal:

Q3. Draw a neat labelled diagram of reflection of light from a plane reflecting surface using plane wavefront

Q4. Define angle of polarisation and state Brewster’s law.

• Angle of Polarisation: The particular angle of incidence at which the reflected light is completely plane polarized is called the angle of polarization or the polarizing angle.
• Brewster’s Law: It states that “The tangent of the polarizing angle is equal to the refractive index of the material of the surface from which reflection is taking place.”

Q5. Using Huygens’ principle, explain the construction of a plane wavefront

• Consider a plane wavefront ABCDE at any instant. According to Huygens’ principle, each point on a wavefront acts as a secondary source of light producing secondary wavelets in all directions.
• Let c be the velocity of light in air and ‘t’ be the time after which position of the wavefront is to be found. During time ‘t’ the light wave will travel a distance of ‘ct’. To find the position and shape of the wavefront after a time ‘t’, a number of spheroids of radius ‘ct’ are drawn with their centres A, B, C, D, and E.
• The tangential envelope (surface) joining the points A’, B’, C’, D’ and E’ in the forward direction is the new wavefront at that instant.  The secondary wavelets are effectively only in the direction of wave normal.  Therefore, a backward wavefront is absent.

Short Answers – II (3 Marks)

Q1. State Huygens’ principle and explain the construction of spherical wavefront.

• Huygen’s principle:
• Every point on a wavefront behaves as if it is a secondary source of light sending secondary waves in all possible directions.
• The new secondary wavelets are more effective in the forward direction only.
• The envelope (tangent) of all the secondary wavelets at a given instant in the forward direction gives the new wavefront at that instant.
• Construction of Spherical wavefront:
• Consider a point source O of light giving rise to a spherical wavefront ABCDE at any instant. According to Huygens’ principle, each point on a wavefront acts as a secondary source of light producing secondary wavelets in all directions.
• Let c be the velocity of light in air and ‘t’ be the time after which position of the wavefront is to be found. During time ‘t’ the light wave will travel a distance of ‘ct’. To find the position and shape of the wavefront after a time ‘t’, a number of spheroids of radius ‘ct’ are drawn with their centres A, B, C, D, and E.
• The tangential spherical envelope (surface) joining the points A’, B’, C’, D’ and E’ in the forward direction is the new wavefront at that instant.  The secondary wavelets are effectively only in the direction of wave normal.  Therefore, a backward wavefront is absent.

Q2. Write merits and demerits of Huygens’ wave theory of light.

• Merits of Huygen’s Wave Theory of Light:
• On the basis of wave theory, the phenomenon of reflection, refraction, diffraction, interference, polarization and total internal reflection of light could be explained.
• Wave theory correctly predicted that the velocity of light in an optically denser medium is less than that in a rarer medium which is in agreement with experimental results.
• On the basis of wave theory, partial reflection and refraction of light could be explained without making contradictory hypotheses.
• Demerits of Huygens’s Wave Theory of Light:
• Wave theory assumes the existence of luminiferous ether. However, experimental attempts to detect the presence of ether particle were unsuccessful.
• Huygen’s theory could not explain the rectilinear propagation of light.
• The phenomena of the photoelectric effect, Crompton effect in Modern Physics cannot be explained using wave theory.

Q3. Explain the phenomenon of polarisation of light by reflection.

• Malus showed that when a beam of unpolarized light is reflected from a nonmetallic surface, the reflected light is partially plane polarized.
• The degree of polarization depends on the angle of incidence. The particular angle of incidence at which the reflected light is completely plane polarized is called the angle of polarization or the polarizing angle.
• The vibrations of the reflected plane polarized light are found to be perpendicular to the plane of incidence

Q4. State and prove Brewster’s law.

• Brewster’s law states that “The tangent of the polarizing angle is equal to the refractive index of the material of the surface from which reflection is taking place.”

Mathematically,     μ = tan ip

ip = angle of incidence and r = angle of refraction

• Proof:
• Let us consider the unpolarized monochromatic light incident in air at the polarizing angle ip on the plane surface XY of the transparent medium of refractive index μ. Experimentally Brewster proved that ∠ SQR = 90°.

Q5. What are different types of wavefronts? How are they produced?

• Spherical Wavefront:

• Consider a point source of light S placed in air.  The source will emit waves of light in all possible directions.
• If the velocity of light in air is c, then in time ‘t’, each wave will cover a distance ct. Therefore, at the end of time interval ‘t’  the light emitted, by, the source will reach at all points as a sphere with centre S and radius equal to ct.
• All the points on the surface of this sphere are in the same phase.  Such a spherical surface is called spherical. wavefront. Thus spherical wavefront is given by a point source.
• Plane Wavefront:

• Consider a spherical wavefront of a very large radius.  At a very large distance from a point source of light, the spherical wavefront is so large that a small part of its surface can be considered as a plane surface i.e. a plane wavefront.
• Light from the sun reaches the surface of the earth in the form of plane wavefronts.
• Theoretically, the plane wavefront is obtained only at infinite distance from a point source.
• Cylindrical Wavefront:

• If a source of light is linear i.e. in the form of a slit the wavefront originating from it has the shape of a cylinder.  Such a wavefront is called a cylindrical wavefront.

Q6. Explain the concept of the wavefront and wave normal.

• Wavefront:
• A wavefront is defined as the locus of all the points of a medium, which receives light wave disturbance simultaneously so that all these points are, in the same phase.
• Wave Normal:
• A perpendicular drawn to the surface of a wavefront at any point in the direction of propagation of light is called as wave normal.
• The direction of propagation of a wave front is given by a ray of light.  Therefore, a wave normal represents a ray of light.

 Maharashtra State Board > Science >  Wave Theory of Light > You are Here

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