Wave Optics — CBSE Class 12 board PYQs

In a Young's double slit experiment in air, the fringe width is found to be $0.44$ mm. If the entire setup is immersed in water $\left(n=\frac{4}{3}\right)$, the fringe width will be

Assertion (A): In a Young's double-slit experiment, interference pattern is not observed when two coherent sources are infinitely close to each other.
Reason (R): The fringe width is proportional to the separation between the two sources.

A ray of monochromatic light propagating in air is incident on the surface of water. Which of the following will be the same for the reflected and refracted rays?

Assertion (A): In Young's double slit experiment all fringes are of equal width.
Reason (R): The fringe width depends upon wavelength of light $(\lambda )$ used, distance of screen from plane of slits $(D)$ and slit separation $(d)$.

Distinguish between unpolarized and linearly polarized light.

What is unpolarized light? Explain with the help of a suitable ray diagram how an unpolarized light can be polarized by reflection from a transparent medium. Write the expression for Brewster angle in terms of the refractive index of the denser medium.

Two narrow slits are illuminated by a single monochromatic source. Name the pattern obtained on the screen. One of the slits is now completely covered. What is the name of the pattern now obtained on the screen? Draw the intensity pattern obtained in the two cases. Also write two …

Two slits in Young's double slit experiment are illuminated by two different lamps emitting light of the same wavelength. Will you observe the interference pattern? Justify your answer. Find the ratio of intensities at two points on a screen in Young's double slit experiment, whe …

What happens to the interference pattern when two coherent sources are
(a) infinitely close, and
(b) far apart from each other?

How will the interference pattern in Young's double-slit experiment be affected if:
(i) the screen is moved away from the plane of the slits;
(ii) the source slit is moved away from the plane of the slits;
(iii) the phase difference between the light waves emanating from the two …

Define the wavefront of a travelling wave. Using Huygens' principle, obtain the law of refraction at a plane interface when light passes from a denser to a rarer medium.

What is the effect on the interference fringes in Young's double slit experiment due to each of the following operations? Justify your answers.
(a) The screen is moved away from the plane of the slits.
(b) The separation between the slits is increased.
(c) The source slit is move …

Define the term wavefront. Using Huygens' wave theory, verify the law of reflection.

Define the term "refractive index" of a medium. Verify Snell's law of refraction when a plane wavefront is propagating from a denser to a rarer medium.

(a) If one of the two identical slits producing interference in Young's experiment is covered with glass, so that the light intensity passing through it is reduced to $50\%$, find the ratio of the maximum and minimum intensity of the fringe in the interference pattern.
(b) What k …

A plane wavefront propagating from a rarer into a denser medium is incident at an angle of incidence $i$ on a refracting surface. Draw a diagram showing the incident wavefront and the refracted wavefront. Hence verify Snell's law of refraction.

State Brewster's law.

(i) Derive Snell's law on the basis of Huygens' wave theory when light is travelling from a denser to a rarer medium.
(ii) Draw sketches to differentiate between a plane wavefront and a spherical wavefront.

Find an expression for the intensity of transmitted light when a polaroid sheet is rotated between two crossed polaroids. In which position of the polaroid sheet will the transmitted intensity be maximum?

(a) In a double slit experiment using light of wavelength $600$ nm, the angular width of the fringe formed on a distant screen is $0.1^{\circ }$. Find the spacing between the two slits.
(b) Light of wavelength $5000\text{A˚}$ propagating in air gets partly reflected from the su …

A parallel beam of light of $450$ nm falls on a narrow slit and the resulting diffraction pattern is observed on a screen $1.5$ m away. It is observed that the first minimum is at a distance of $3$ mm from the centre of the screen. Calculate the width of the slit.

(a) What is linearly polarized light? Describe briefly, using a diagram, how sunlight is polarised.
(b) Unpolarised light is incident on a polaroid. How does the intensity of transmitted light change when the polaroid is rotated?

(a) Why are coherent sources necessary to produce a sustained interference pattern?
(b) In Young's double slit experiment using monochromatic light of wavelength $\lambda$, the intensity of light at a point on the screen where the path difference is $\lambda$ is $K$ units. Find o …

Use Huygens' principle to explain the formation of the diffraction pattern due to a single slit illuminated by a monochromatic source of light. When the width of the slit is made double the original width, how would this affect the size and intensity of the central diffraction ba …

What is a wavefront? What is the geometrical shape of a wavefront of light emerging out of a convex lens, when a point source is placed at its focus? Using Huygens' principle show that, for a parallel beam incident on a reflecting surface, the angle of reflection is equal to the …

A slit of width $0.6$ mm is illuminated by a beam of light consisting of two wavelengths $600$ nm and $480$ nm. The diffraction pattern is observed on a screen $1.0$ m from the slit. Find:
(i) the distance of the second bright fringe from the central maximum pertaining to light o …

(a) Describe any two characteristic features which distinguish between interference and diffraction phenomena. Derive the expression for the intensity at a point of the interference pattern in Young's double slit experiment.
(b) In the diffraction due to a single slit experiment, …

(a) Define a wavefront. Using Huygens' principle, verify the laws of reflection at a plane surface.
(b) In a single slit diffraction experiment, the width of the slit is made double the original width. How does this affect the size and intensity of the central diffraction band? E …

Explain with a diagram how plane polarized light can be produced by scattering of sunlight. An incident beam of light of intensity $I_0$ is made to fall on a polaroid A. Another polaroid B is so oriented with respect to A that there is no light emerging out of B. A third polaroid …

(a) In Young's double slit experiment, a monochromatic source of light S is kept equidistant from the slits $S_1$ and $S_2$. Explain the formation of dark and bright fringes on the screen. (b) A beam of light consisting of two wavelengths, $650$ nm and $520$ nm, is used to obtain …

(a) Distinguish between unpolarized light and linearly polarized light. How does one get linearly polarised light with the help of a Polaroid?
(b) A narrow beam of unpolarised light of intensity $I_0$ is incident on a Polaroid $P_1$. The light transmitted by it is then incident o …

(a) Explain two features to distinguish between the interference pattern in Young's double slit experiment and the diffraction pattern obtained due to a single slit.
(b) A monochromatic light of wavelength $500$ nm is incident normally on a single slit of width $0.2$ mm to produc …

(a) In Young's double slit experiment, deduce the conditions for (i) constructive, and (ii) destructive interference at a point on the screen. Draw a graph showing the variation of intensity in the interference pattern against position 'x' on the screen. (b) Compare the interfere …

(a) Why does unpolarised light from a source not show a variation in intensity when viewed through a Polaroid which is rotated? Show with the help of a diagram how unpolarised light from the sun gets linearly polarised by scattering.
(b) Three identical Polaroid sheets $P_1$, …

(a) Derive an expression for the path difference in Young's double slit experiment and obtain the condition for constructive and destructive interference at a point on the screen.
(b) The intensity at the central maxima in Young's double slit experiment is $I_0$. Find out the int …

(a) Using Huygens' construction of secondary wavelets explain how a diffraction pattern is obtained on a screen due to a narrow slit on which a monochromatic beam of light is incident normally.
(b) Show that the angular width of the first diffraction fringe is half that of the ce …

(a) Show, giving a suitable diagram, how unpolarized light can be polarized by reflection.
(b) Two polaroids $P_1$ and $P_2$ are placed with their pass axes perpendicular to each other. Unpolarised light of intensity $I_0$ is incident on $P_1$. A third polaroid $P_3$ is kept in b …

State Huygens' principle. Show, with the help of a suitable diagram, how this principle is used to obtain the diffraction pattern by a single slit. Draw a plot of the intensity distribution and explain clearly why the secondary maxima become weaker with increasing order $(n)$ of …

What are coherent sources? Why are coherent sources required to produce interference of light? Give an example of interference of light in everyday life. In Young's double slit experiment, the two slits are $0.03$ cm apart and the screen is placed at a distance of $1.5$ m away fr …

State the condition under which the phenomenon of diffraction of light takes place. Derive an expression for the width of the central maximum due to diffraction of light at a single slit. A slit of width 'a' is illuminated by monochromatic light of wavelength $700$ nm at normal i …

(a) In Young's double slit experiment, describe briefly how bright and dark fringes are obtained on the screen kept in front of a double slit. Hence obtain the expression for the fringe width.
(b) The ratio of the intensities at minima to the maxima in the Young's double slit exp …

(a) Describe briefly how a diffraction pattern is obtained on a screen due to a single narrow slit illuminated by a monochromatic source of light. Hence obtain the conditions for the angular width of the secondary maxima and secondary minima. (b) Two wavelengths of sodium light o …

(a) (i) A plane light wave propagating from a rarer into a denser medium is incident at an angle 'i' on the surface separating the two media. Using Huygens' principle, draw the refracted wave and hence verify Snell's law of refraction. (ii) In a Young's double slit experiment, th …

(b) (i) Discuss briefly diffraction of light from a single slit and draw the shape of the diffraction pattern. (ii) An object is placed between the pole and the focus of a concave mirror. Using the mirror formula, prove mathematically that it produces a virtual and an enlarged im …