Answer the following questions
(a) 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?
(b) In what way is diffraction from each slit related to the interference pattern in a double-slit experiment?
(c) When a tiny circular obstacle is placed in the path of light from a distant source, a bright spot is seen at the centre of the shadow of the obstacle. Explain why?
(d) Two students are separated by a 7 m partition wall in a room 10 m high. If both light and sound waves can bend around obstacles, how is it that the students are unable to see each other even though they can converse easily
(e) Ray optics is based on the assumption that light travels in a straight line. Diffraction effects (observed when light propagates through small apertures/slits or around small obstacles) disprove this assumption. Yet the ray optics assumption is so commonly used in understanding location and several other properties of images in optical instruments. What is the justification?

Explanation

(a) In a single slit diffraction experiment, if the width of the slit is made double the original width, then the size of the central diffraction band reduces to half and the intensity of the central diffraction band increases up to four times.
(b) The interference pattern in a double-slit experiment is modulated by diffraction from each slit. The pattern is the result of the interference of the diffracted wave from each slit.
(c) When a tiny circular obstacle is placed in the path of light form a disctance source, a bright spot is seen at the centre of the shadow of the obstacle. This is because ligth waves are diffracted from the edge of the circular, obstacle, which interfers constructively at the centre of the shadow. This constructive interference prodcues a bright spot.
(d) Bending of waves by obstacles by a large anlge is possible when the size of the obstacle is compable to the wavelength of the waves.
On the one hand, the wavelength of the light waves is too small in comparison to the size of the obstacle. Thus, the diffraction angel will be very wall is comaprable to the wavelength of the sound. waves. Thus, the bending of the wave takes place at a large angle, Hence the students are able to hear each other.
(e) The justification is that in ordinary optical instruments , the size of the apeture involved is much larger than the wavelength of the ligth used.