Light can illuminate objects around corners. This is due to the bending of light, which is known as diffraction. This section of the NCERT Solutions for Class 12 Wave Optics chapter covers the diffraction of light in detail.
a. The Single Slit
In Young’s experiment, it was evident that a narrow slit behaves as a new source from which light bends and illuminates the area around. The light appears to bend around corners and illuminate areas where a shadow is expected to exist. When the two slits in Young’s experiment are replaced by one narrow slit, an illuminated region appears with the intensity of light being the strongest at the centre and fading away towards the edges.
b. Seeing the Single Slit Diffraction Pattern
To see the single-slit diffraction pattern at home, two razor blades and one electric bulb with a straight filament can be used. The two blades have to be positioned in such a way that the edges are parallel and have a narrow slit between them. The slit has to be placed parallel to the filament and directly in front of the eye. The pattern should now appear with its bright and dark regions. The pattern may show some colours depending on the wavelength of the bands. The fringes can be seen more clearly by placing a blue or red filter.
c. Resolving Power of Optical Instruments
Consider a beam of light hitting a convex lens. If the lens is well adjusted for aberrations, then the beam will focus on a single point. However, due to diffraction, the beam gets focused to a region of the finite area instead of a point. In such circumstances, the effects caused by diffraction are considered by taking a plane wave incident on a circular aperture and then on a convex lens. The analysis of the corresponding diffraction pattern is similar to the analysis obtained from the single-slit diffraction pattern. The pattern on the focal plane consists of a bright region in the centre with concentric dark and bright rings surrounding it. The resolving power of an optical instrument is the reciprocal of the distance or angular separation between two objects that can be resolved when looked at through the optical instrument.
The resolving power of a telescope is . A large diameter d gives a better resolution of the image.
The resolving power of a microscope is , where n is the refractive index of the medium between the object and the aperture. A large value of the numerical aperture nsinθ results in a high resolution of the image.
d. The Validity of Ray Optics
Consider a slit with aperture a. The angular size of the central bright region in the diffraction pattern is given by λ/a. After covering a distance z, the diffracted beam reaches a width zλ/a. Equating zλ/a with a, the distance is obtained beyond which divergence of the beam becomes significant. Therefore, the distance z = a2/λ is known as the Fresnel distance, defined as the distance at which the spreading due to diffraction becomes comparable to the width of the slit. If the distance is lesser than zF, the spreading due to diffraction is smaller than the beam. If the distance is larger than zF, the spreading due to diffraction begins to dominate because of ray optics.