CBSE Class 12 · Wave OpticsLong Answer

WhatsApp Email
(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 image.

Solution

(i) A plane wavefront on a single slit (width ) produces secondary wavelets (Huygens). Along the axis they reinforce to give a bright central maximum; for direction the path difference gives minima at and weak secondary maxima at . The intensity shape is a dominant central band (twice as wide) flanked by rapidly decreasing side bands (see figure).
(ii) For a concave mirror take negative; an object between pole and focus has . From the mirror formula

Since , has the sign that makes positive, i.e. the image is formed behind the mirror — it is . The magnification is

with this gives , so the image is (and erect).

CBSE Class 12 Board · Subjective

More board questions on Wave Optics

  1. In a Young's double slit experiment in air, the fringe width is found to be mm. If the entire setup is immersed in water , the fringe width will be
    CBSE 2024View solution →
  2. 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.
    CBSE 2024View solution →
  3. 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?
    CBSE 2023View solution →
  4. Assertion (A): In Young's double slit experiment all fringes are of equal width.
    Reason (R): The fringe width depends upon wavelength of light used, distance of screen from plane of slits and slit separation .
    CBSE 2023View solution →
  5. What happens to the interference pattern when two coherent sources are
    (a) infinitely close, and
    (b) far apart from each other?
    CBSE 2023View solution →
  6. 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 …
    CBSE 2022View solution →