Wave Optics — Class 12 Physics PYQs

Which one of the following correctly represents the change in wave characteristics (all in vacuum) from microwaves to X-rays in electromagnetic spectrum ?
Speed Wavelength Frequency
(A) Remains same Decreases Remains same
(B) Remains same Decreases Increases
(C) Increases Increases Decreases
(D) Remains same Increases Remains same

Show the refraction of light wave at a plane interface using Huygens' principle and prove Snell's law.

In a diffraction experiment, the slit is illuminated by light of wavelength 600 nm. The first minimum of the pattern falls at $\theta =30^{\circ }$. Calculate the width of the slit.
OR
(b) In a Young's double-slit experiment, two light waves, each of intensity $I_o$, interfere at a point, having a path difference $\frac{\lambda }{8}$ on the screen. Find the intensity at this point.

In a double-slit experiment, 6th dark fringe is observed at a certain point of the screen. A transparent sheet of thickness t and refractive index n is now introduced in the path of one of the two interfering waves to increase its phase by $2\pi (n-1)t/\lambda$. The pattern is shifted and 8th bright fringe is observed at the same point. Find the relation for thickness t in terms of n and $\lambda$.

What are coherent sources ? Why are they necessary for observing a sustained interference pattern ?
(ii) Lights from two independent sources are not coherent. Explain.
(iii) Two slits 0.1 mm apart are arranged 1.20 m from a screen. Light of wavelength 600 nm from a distant source is incident on the slits.
(1) How far apart will adjacent bright interference fringes be on the screen ?
(2) Find the angular width (in degree) of the first bright fringe.
OR
(b) (i) Define a wavefront. An incident plane wave falls on a convex lens and gets refracted through it. Draw a diagram to show the incident and refracted wavefront.
(ii) A beam of light coming from a distant source is refracted by a spherical glass ball (refractive index 1.5) of radius 15 cm. Draw the ray diagram and obtain the position of the final image formed.

Monochromatic light of frequency 5.0 × 10${}^{14}$ Hz passes from air into a medium of refractive index 1.5. Find the wavelength of the light (i) reflected, and (ii) refracted at the interface of the two media.

Two waves, each of amplitude 'a' and frequency '$\omega$' emanating from two coherent sources of light superpose at a point. If the phase difference between the two waves is $\varphi$, obtain an expression for the resultant intensity at that point.
OR
(b) What is the effect on the interference pattern in Young's double-slit experiment when (i) the source slit is moved closer to the plane of the slits, and (ii) the separation between the two slits is increased ? Justify your answers.

Give any two differences between the interference pattern obtained in Young's double-slit experiment and a diffraction pattern due to a single slit.
(ii) Draw an intensity distribution graph in case of a double-slit interference pattern.
(iii) In Young's double-slit experiment using monochromatic light of wavelength $\lambda$, the intensity of light at a point on the screen, where path difference is $\lambda$, is K units. Find the intensity of light at a point on the screen where the path difference is $\lambda /6$.

State Huygens' principle. A plane wave is incident at an angle i on a reflecting surface. Construct the corresponding reflected wavefront. Using this diagram, prove that the angle of reflection is equal to the angle of incidence.
(ii) What are the coherent sources of light ? Can two independent sodium lamps act like coherent sources ? Explain.
(iii) A beam of light consisting of a known wavelength 520 nm and an unknown wavelength $\lambda$, used in Young's double slit experiment produces two interference patterns such that the fourth bright fringe of unknown wavelength coincides with the fifth bright fringe of known wavelength. Find the value of $\lambda$.

OR
(b) A plane wavefront of light of wavelength 'λ' is incident normally on a narrow slit of width 'a' and a diffraction pattern is observed on a screen at a distance 'D' from the slit.
(i) Depict the intensity distribution in the pattern observed.
(ii) Obtain the expression for the first maximum from the central maximum.