(a) when width (a) of single slit is made double, the half angular width of central maximum which is `lambda//a`, reduces to half. The intensity of central maximum will become `4 times`. This is because area of central diffraction band would become `1//4th`.
(b) If width of each slit is of the order of `lambda`, then interference pattern in the double slit experiment is modified by the diffraction pattern from each of the two slits.
( c) This is becasue waves diffracted from the edges of circular obstacle interfere constructively at the centre of the shadow resulting in the formation of a bright spot.
(d) For diffraction of waves by obstacle//aperture, through a large angle, the size of obstacle//aperture should be comparable to wavelengt. This follows from `sin theta = lambda//a`.
For light, `lambda ~~ 10^(-7)m` and sizze of wall `a ~~ 10m. :. sin theta = (lambda)/(a) = (10^(-7))/(10) = 10^(-8) :. theta rarr 0`.
i.e light goes almost unbent. The students are thus unable to see each other.
For sound waves of frequency `~~ 1000 Hz, lambda = (v)/(n) = (330)/(1000) = 0.33m`
`sin theta = (lambda)/(a) = (0.33)/(10) = 0.033`
`:. theta` has a definite values i.e. sound waves bend around the partition. Hence students can cinverse easily.
(e) The ray optics assumption is used in understanding loaction and several other properties of image in optical intstruments. This is because typical sizes of paertures invloved in ordinary optical instruments are much larger than the wavelength of light. Therefore, diffraction or bending of waves is of no significance.
