
Monochromatic light of wavelength is incident from air on a water surface. What are the wavelength, frequency and speed of reflected light? Take,

Important Points to Remember in Chapter -1 - Wave Optics from NCERT PHYSICS PART 2 TEXTBOOK FOR CLASS 12 Solutions
(i) In a propagating wave, the locus of points, which oscillate in phase is called a wavefront. Thus, a wavefront is defined as a surface of constant phase.
(ii) The wavefronts of a point source will be spherical in shape and that of a distance source will be planar in shape.
(iii) According to Huygens principle, each point of the wavefront is the source of a secondary disturbance and the wavelets referred to as secondary 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 spheres, we obtain the new position of the wavefront.
(iv) The phenomenon of refraction of light could not be explained by the corpuscular model of light proposed by Newton, but it was successfully explained by the wave nature of light proposed by Huygens.
2. Doppler effect in light:
(i) The Doppler effect: The changes in the frequency of light due to the motion of the source is called as Doppler effect. When the source is moving towards the observer, the frequency increases (blue shift), and when the source is moving away, the frequency decreases (red shift).
(ii) The fractional change is the frequency in Doppler effect is given by, . The formula given above is valid only when the speed of the source is small compared to that of light.
3. Superposition of waves:
(i) Superposition of waves: When there are two coherent sources of light of wavelength (), if the path difference at a point from the two sources is , where is an integer, then constructive interference occurs, but when it is , destructive interference occurs.
(ii) Intensity is proportional to the amplitude, so at constructive interference, the amplitude doubles and intensity becomes four times.
(iii) If the phase difference of sources of amplitude () and intensity () at a point is, then the amplitude of the resultant wave is and the resultant intensity is .
4. Young's Double slit experiment:
(i) In Young’s Double slit experiment, the path difference between two sources is approximately given as , where is the screen distance, is the slit separation and is the distance of the point on the screen from the centre.
(ii) At , intensity is maximum (bright fringe) and at , intensity is minimum (dark fringe). Fringe width,
5. Single slit diffraction:
(i) In single slit diffraction, the brightest spot is seen at . At , subsequent maxima are seen, and at , minima are seen. Where is the slit width.
(ii) When a lens of focal length () is placed in front of the slit, the separation of the bright fringes on the screen will be .
(iii) The radius of the bright spot formed by a lens is given by, , where is the focal length of the lens and is the diameter of the lens.
6. Resolving power of optical instruments:
(i) The angular separation of two faraway objects to be viewed clearly by a lens is given by,
(ii) The resolution of a microscope is given by, , where is the angle made by the principal axis and the tip of the lens with object, and is the refractive index of the medium. is called numerical aperture.
(iii) The Fresnel distance is the distance from a lens beyond which the diffraction effects of the lens are comparable to the size of the lens. It is given by the formula, , where is the radius of the lens.
7. Polarization of light:
(i) Plane polarized wave is the wave in which the disturbances at all the points occur in the same plane.
(ii) A polaroid is a material which allows disturbances in only one direction called pass axis, thus producing a plane polarized wave. It also reduces the intensity of the unpolarized wave by half.
(iii) According to Malus law, if a polarized light of intensity () falls on a polaroid whose pass axis makes an angle of with the plane of incident light, then the intensity of the emitted light will be,
(iv) The angle of incidence at which the reflected wave will be totally polarized is called as the Brewster’s angle and it is given by, . In this situation, the reflected and the refracted waves will be perpendicular to each other.