Unit VI: Optics Chapter–9: Ray Optics and Optical Instruments
Ray Optics: Reflection of light, spherical mirrors, mirror formula, refraction of light, total internal reflection and optical fibers, refraction at spherical surfaces, lenses, thin lens formula, lens maker’s formula, magnification, power of a lens, combination of thin lenses in contact, refraction of light through a prism. Optical instruments: Microscopes and astronomical telescopes (reflecting and refracting) and their magnifying powers.
Chapter–10: Wave optics: Wave front and Huygen’s principle, reflection and refraction of plane wave at a plane surface using wave fronts. Proof of laws of reflection and refraction using Huygen’s principle. Interference, Young's double slit experiment and expression for fringe width (No derivation final expression only), coherent sources and sustained interference of light, diffraction due to a single slit, width of central maxima (qualitative treatment only).
PHYSICS
CLASS 12
Wave Optics
Basic Questions
INTRODUCTION
The questions given below are the basic questions which every student must know. If these questions are prepared then further study of numericals and other concepts will be easier.
Q1. Define a wavefront.
A locus of all those points I medium who oscillate in same phase, is called a wavefront or a wavefront is defined as a surface of constant phase.
Q2. Write Huygen's principles.
According to Huygens principle, 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. if we draw a common tangent to all these wavelet spheres, we obtain the position of the new wavefront (secondary) at a later time.
Q3. Use Huygen's principles to explain reflection of a plane wavefront. Hence prove laws of reflection.
Consider a plane wave AB incident at an angle i on a reflecting surface MN. If v represents the speed of the wave in the medium and if τ represents the time taken by the wavefront to advance from the point B to C then the distance BC = vτ
In order the construct the reflected wavefront we draw a sphere of radius vτ from the point A as shown in Figure. Let CE represent the tangent plane drawn from the point C to this sphere. Obviously AE = BC = vτ
If we now consider the triangles EAC and BAC we will find that they are congruent and therefore, the angles i and r would be equal. This is the law of reflection.
Q4. (a) Use Huygen's principles to explain refraction of a plane wavefront from a rarer to denser medium. Hence prove Snell's law.
Let PP′ represent the surface separating medium 1 and medium 2. Let v1 and v2
represent the speed of light in medium 1 and medium 2, respectively.
v2<v1
We assume a plane wavefront AB propagating in the direction A′A incident on the interface at an angle i. Let τ be the time taken by the wavefront to travel the distance BC. Thus, BC = v1.τ
In order to determine the shape of the refracted wavefront, we draw a sphere of radius v2.τ from the point A in the second medium (the speed of the wave in the second medium is v2). Let CE represent a tangent plane drawn from the point C on to the sphere. Then, AE = v2.τ and CE would represent the refracted wavefront.
If we now consider the triangles ABC and AEC, we obtain
where i and r are the angles of incidence and refraction, respectively. Thus we get
But refractive index n=c/v hence n2/n1=v1/v2
Hence sini/sinr = n2/n1
Q4. (b) Use Huygen's principles to explain refraction of a plane wavefront from a denser to rarer medium. Hence prove Snell's law.
Explanation is similar to the above question keeping in mind v2>v1.
Q5. Draw the emerging wave front when a plane wavefront fall on a
prism.
Answer
Convex lens
Answer
Concave lens
Do yourself
Q5. Draw the reflected wave front when a plane wavefront fall on a
Concave mirror
Answer
Diverging mirror
Do yourself
Question: What are coherent sources of light?
Answer: Two sources are said to be coherent if they emit lights of same frequency and same wavelength and they have zero OR constant phase difference.
Question: Find conditions for constructive and destructive interference of light.
Answer: Let the phase difference between the two displacements at a point P be φ. Thus, if the displacement produced by S1 is given by y1 = a cos (ωt)
then, the displacement produced by S2 would be y2 = a cos (ωt + φ )
Then the resultant displacement will be given by y = y1 + y2
y = a [cos ωt + cos (ωt +φ)]
= 2 a cos (φ/2) cos (ωt + φ/2)
The amplitude of the resultant displacement is 2a cos (φ/2) and
therefore the intensity at that point will be
I =k4a2cos2(φ/2) = 4 I0 cos2(φ/2)
If φ = 0, ± 2 π, ± 4 π,… which corresponds to the path difference,
S1P ~ S2P = nλ where (n = 0, 1, 2, 3,...)
we will have constructive interference leading to maximum intensity.
On the other hand, if φ = ± π, ± 3π, ± 5π … which corresponds to the path difference, S1P ~ S2P = (n+1/2 )λ
where (n = 0, 1, 2, 3, ...), we will have destructive interference leading to zero intensity.
Evaluation:
Q.1. define interference of light.
Q.2 The phase difference between two waves superposing at a point is λ/2. Tell whether the interference is constructive or destructive?
Q.3 What are coherent sources of light?
Q4. In double-slit experiment using monochromatic light of wavelength λ, the intensity of light at a point on the screen where the path difference is λ, is K units. What is the intensity of light at a point where path difference is λ/3?
HW
Q.1. find resultant intensity at a point when two similar waves superpose.
Q.2. define interference of light.
Q.3. write condition for constructive and destructive interference at a point on screen when two similar waves superpose.
Question: What do you mean by the sustained interference of light. Write a condition for it.
Answer: If the intensity of the fringes of interference pattern on the screen does not vary with time, it remains constant or the same, then it is called sustained interference.
To obtain sustained interference, coherent sources of light are needed and the two slits should be very narrow and close.
Question: Define fringe width. On what factors does it depend?
Answer: The separation between two consecutive bright or dark fringes is called fringe width.
Linear fringe width = Dλ/d
Linear fringe width depends on distance of screen from the slits D, wavelength of the light used λ and separation between the slits d.
Angular fringe width = λ/d
Angular fringe width depends on wavelength of the light used λ and separation between the slits d.
Question: Draw interference pattern of young's double slit experiment.
Answer:
Question: Define diffraction and give one example.
Answer: The bending of light at sharp edges or corners of obstacles is known as diffraction. Due to diffraction the light reaches in geometrical shadow regions.
It is observed on cassette discs.
Question: Write a formula for width of Central Maxima in the single slit diffraction pattern.
Answer: Linear width = 2Dλ/a
Question: Draw the single slit diffraction pattern.
Question: A parallel beam of light of wavelength 500 nm falls on a narrow slit and the resulting diffraction pattern is observed on a screen 1 m away. It is observed that the first minimum is at a distance of 2.5 mm from the centre of the screen. Find the width of the slit.
Question: Write any two differences between the double slit interference pattern and single slit diffraction pattern.
Answer: (i) The interference pattern has a number of equally spaced bright and dark bands.
The diffraction pattern has a central bright maximum which is twice as wide as the other maxima. The intensity falls as we go to successive maxima away from the centre, on either side. (ii) We calculate the interference pattern by superposing two waves originating from the two narrow slits.
The diffraction pattern is a superposition of a continuous family of waves originating from each point on a single slit.
(iii) For a single slit of width a, the first null of the interference pattern occurs at an angle of λ /a. At the same angle of λ /a, we get a maximum (not a null) for two narrow slits separated by a distance 'a'.
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