(i) Its cost is very high due to scarity of large and flawless calcite crystals
(ii) Due to extraordinary ray passing obliquely through it the emergent ray is always displaced a little to one side.
(iii) The effective field of view is quite limited
(iv) Light emerging out of it is not uniformly plane polarised.

(i) Similar to a rectangular slit, when a circular aperture or opening (like a lens or the iris of our eye) forms an image of a point object, the image formed will not be a point but a diffraction pattern of concentric circles that become fainter while moving away from the center as shown in Figure. These are known as Airy's discs
\(asin\theta =1.22\lambda \) 

(ii) Here, the numerical value 1.22 comes for central "maximum formed by circular apertures.
For small angles, sin θ = θ
\(a\theta =1.22\lambda \) 
Rewriting further,
\(\theta =\cfrac { 1.22\lambda }{ a } \ and \cfrac { { r }_{ o } }{ f } =\cfrac { 1.22\lambda }{ a } \)
\({ r }_{ o }=\cfrac { 1.22\lambda f }{ a } \)

(i) For points of maxima, the slit is to be divided into an odd number of equal parts so that one part remains un-canceled making the point P appear bright.
The condition for the first maximum is,
\(\cfrac { a }{ 3 } sin\theta =\cfrac { \lambda }{ 2 } \) (or) \(asin\theta =\cfrac { 3\lambda }{ 2 } \) 
The condition for the second maximum is
\(\cfrac { a }{ 5 } sin\theta =\cfrac { \lambda }{ 2 } \) (or) \(asin\theta =\cfrac { 5\lambda }{ 2 } \) 
The condition for the third maximum is,
\(\cfrac { a }{ 7 } sin\theta =\cfrac { \lambda }{ 2 } \) (or) \( asin\theta =\cfrac { 7\lambda }{ 2 } \)
In the same way, the condition for n^th maximum is 
\(asin\theta =\left( 2n+1 \right) \cfrac { \lambda }{ 2 } \) (n^th maximum)
where, n = 0, 1, 2, 3, ... , is the order of diffraction maximum.
(ii) The central maximum is called the order maximum. The points of the maximum intensity lie nearly midway between the successive minima.

(i) The distance D between the screen and douhle slit should be as large as possibie.
(ii) The wavelength \(\lambda\) of light used must be as long as possible.
(iii) The distance d between the two slits must be as small as possible.