A converging thin lens of focal length f is cut along a plane that contains the optical axis of the lens and a small black plate of thickness $δ$ is placed between the two half lenses as shown in fig-1. A point – like source emitting monochromatic light of wavelength $λ$ is located on the optical axis, a distance p from the lens. One of the cases where p > f and a screen at a distance H placed to catch the interference pattern in shown in fig 2. For all cases assume paraxial rays only and H >> $δ$ >> $λ$

Column–I Column–II
Calculation of number of fringes formed on screen
Column–III
Information required to calculate number of fringes

I) p = 20 cm, f = 10 cm, $δ = 1 m m, λ = 0.5, μ m H = 50 c m$
which is sufficiently large as shown in fig.2
i) Number of fringes formed on screen is finite and non-zero p) There is no interference pattern on screen at given value of H but there will be if H is increased
II) All parameters in I) are taken except H is made smaller by moving screen towards lens between points A, B marked in Fig. 2 ii) Number of fringes formed on screen is zero q) There is a interference on screen but to calculate number of fringes we need diameter of aperture of lens
III) All parameters in I) are taken except H is made smaller by moving screen towards lens and making it closer to lens than point B iii) Number of fringes formed on screen lies between 40 to 50 r) There is interference on screen and to calculate number of fringes, we don’t need diameter of aperture of lens.
IV) All parameters in I) all taken except p = 5 cm is taken. iv) Number of fringes formed on screen is infinite (assuming screen to be infinitely large) s) There is no interference pattern on screen at given value of h and there will no interference even when H is changed to any value.

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	Column–I		Column–II Calculation of number of fringes formed on screen		Column–III Information required to calculate number of fringes
I)	p = 20 cm, f = 10 cm, $δ = 1 m m, λ = 0.5, μ m H = 50 c m$ which is sufficiently large as shown in fig.2	i)	Number of fringes formed on screen is finite and non-zero	p)	There is no interference pattern on screen at given value of H but there will be if H is increased
II)	All parameters in I) are taken except H is made smaller by moving screen towards lens between points A, B marked in Fig. 2	ii)	Number of fringes formed on screen is zero	q)	There is a interference on screen but to calculate number of fringes we need diameter of aperture of lens
III)	All parameters in I) are taken except H is made smaller by moving screen towards lens and making it closer to lens than point B	iii)	Number of fringes formed on screen lies between 40 to 50	r)	There is interference on screen and to calculate number of fringes, we don’t need diameter of aperture of lens.
IV)	All parameters in I) all taken except p = 5 cm is taken.	iv)	Number of fringes formed on screen is infinite (assuming screen to be infinitely large)	s)	There is no interference pattern on screen at given value of h and there will no interference even when H is changed to any value.