A double-slit interference pattern is product on a screen, as shown in figure, using monochromatic light of wavelength 500 nm. Point P is the location of the central bright fringe, that is produced when light waves arrive in phase without any path difference. A choice of three strips A,B and C of transparent materials with different thickness and refractive indices is available, as shown in the table. These are placed over one or both of the slits, singularly or in conjunction, causing the interference pattern to be shifted across the screen from the original pattern. In Column I, how the strips have been placed, is mentioned whereas in Column II, order of the fringe at point P on the screen that will be produced due to the placement of the strip(s), is shown, Correctly match both the columns.
Film
A
B
C
Thickness (in μm)
5
1.5
0.25
Refractive index
1.5
2.5
2
Column I
Column II
(A)
Only strip B is placed over slit I
(P)
First bright
(B)
Strip Ais placed over slit Iand and strip C is placed over slit II
(Q)
Fourth dark
(C)
Strip A is placed over slit Iand strip B and strip C are placed over slit II in conjunction.
(R)
Fifth dark
(D)
Strip A and strip C are placed over slit I (in conjunction) and strip B is placed over slit II
(S)
Central bright
Which of the following option has the correct combination considering column-I and column-II.
A double-slit interference pattern is product on a screen, as shown in figure, using monochromatic light of wavelength 500 nm. Point P is the location of the central bright fringe, that is produced when light waves arrive in phase without any path difference. A choice of three strips A,B and C of transparent materials with different thickness and refractive indices is available, as shown in the table. These are placed over one or both of the slits, singularly or in conjunction, causing the interference pattern to be shifted across the screen from the original pattern. In Column I, how the strips have been placed, is mentioned whereas in Column II, order of the fringe at point P on the screen that will be produced due to the placement of the strip(s), is shown, Correctly match both the columns.
| Film | A | B | C |
| Thickness (in μm) | 5 | 1.5 | 0.25 |
| Refractive index | 1.5 | 2.5 | 2 |
| Column I | Column II | ||
| (A) | Only strip B is placed over slit I | (P) | First bright |
| (B) | Strip Ais placed over slit Iand and strip C is placed over slit II | (Q) | Fourth dark |
| (C) | Strip A is placed over slit Iand strip B and strip C are placed over slit II in conjunction. | (R) | Fifth dark |
| (D) | Strip A and strip C are placed over slit I (in conjunction) and strip B is placed over slit II | (S) | Central bright |
Which of the following option has the correct combination considering column-I and column-II.
The correct option is A A→R
By using (μ−1)t=nλ,
we can find value of n, that is order of fringe produced at P, if that particular strip has been placed over any of the slit. If two strips are used in conjunction (over each other), path difference due to each is used over difference created. If two strips are used over different slits, their path differences are subtracted to get net path difference. Now,
n1=(μ1−1)t1λ=5
n2=4.5
n3=0.5
For (A), order of the fringe is 4.5,i.e., fifth dark.
For (B), net order is 5−0.5=4.5,i.e., fifth dark.
For (C), net order is 5−0.5+4.5=0,i.e., it is central bright again at P.
For (D), net order is 5+0.5−4.5−1,i.e., first bright.
By using (μ−1)t=nλ,
we can find value of n, that is order of fringe produced at P, if that particular strip has been placed over any of the slit. If two strips are used in conjunction (over each other), path difference due to each is used over difference created. If two strips are used over different slits, their path differences are subtracted to get net path difference. Now,
n1=(μ1−1)t1λ=5
n2=4.5
n3=0.5
For (A), order of the fringe is 4.5,i.e., fifth dark.
For (B), net order is 5−0.5=4.5,i.e., fifth dark.
For (C), net order is 5−0.5+4.5=0,i.e., it is central bright again at P.
For (D), net order is 5+0.5−4.5−1,i.e., first bright.
