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PHXII10:WAVE OPTICS

368064 For sustained interference fringes in double slit experiment, essential conditions /is /are
(a) Sources must be coherent
(b) The intensities of the two sources must be equal.
Here, the correct option / s / is / are

1

b o t h a, b

2 only

a

3 only

b

4 neither

a

nor

b

PHXII10:WAVE OPTICS

368065 In a Young’s double slit experiment, the separation of the two slits is doubled. To keep the same spacing of fringes, the distance $D$ of the screen from the slits should be made

1

\frac{D}{2}

2

\frac{D}{\sqrt{2}}

3

2 D

4

4 D

Explanation:

$β = β^{'} o r \frac{D λ}{d} = \frac{D^{'} λ}{(2 d)} ∴ D^{'} = 2 D$

PHXII10:WAVE OPTICS

368066 The width of two slits in young's experiment are in the ratio of $9 : 4$ . What will be the intensity ratio of maxima and minima in the interference pattern?

1

1 : 1

2

25 : 1

3

5 : 1

4

3 : 2

Explanation:

Intensity ratio $= \frac{(a + b)^{2}}{(a - b)^{2}}$
$∴$ Intensity ratio $= {(\frac{r + 1}{r - 1})}^{2}$
$= {(\frac{\frac{3}{2} + 1}{\frac{3}{2} - 1})}^{2}$
Intensity ratio $= 25 : 1$ .

PHXII10:WAVE OPTICS

368067 The ratio of intensities at two points $P$ and $Q$ on the screen in a Young's double slit experiment where phase difference between two waves of same amplitude are $π / 3$ and $π / 2$ , respectively are

1

3 : 1

2

3 : 2

3

1 : 3

4

3 : 1

Explanation:

Resultant intensity, $I_{net} = I_{1} + I_{2} + 2 \sqrt{I_{1} I_{2}} \cos ϕ$
where $ϕ =$ phase difference.
$I_{1} = I_{0} + I_{0} + 2 I_{0} \cos \frac{π}{3}$ for $(ϕ = \frac{π}{3})$
$I_{1} = 2 I_{0} + 2 I_{0} \times \frac{1}{2} = 3 I_{0}$ $I_{2} = I_{0} + I_{0} + 2 I_{0} \cos \frac{π}{2} = 2 I_{0}$ for $(ϕ = \frac{π}{2})$
Hence, ratio between the two waves
$= \frac{I_{1}}{I_{2}} = \frac{3}{2} \frac{I_{0}}{I_{0}} = \frac{3}{2}$

JEE - 2023

PHXII10:WAVE OPTICS

368064 For sustained interference fringes in double slit experiment, essential conditions /is /are
(a) Sources must be coherent
(b) The intensities of the two sources must be equal.
Here, the correct option / s / is / are

1

b o t h a, b

2 only

a

3 only

b

4 neither

a

nor

b

PHXII10:WAVE OPTICS

368065 In a Young’s double slit experiment, the separation of the two slits is doubled. To keep the same spacing of fringes, the distance $D$ of the screen from the slits should be made

1

\frac{D}{2}

2

\frac{D}{\sqrt{2}}

3

2 D

4

4 D

Explanation:

$β = β^{'} o r \frac{D λ}{d} = \frac{D^{'} λ}{(2 d)} ∴ D^{'} = 2 D$

PHXII10:WAVE OPTICS

368066 The width of two slits in young's experiment are in the ratio of $9 : 4$ . What will be the intensity ratio of maxima and minima in the interference pattern?

1

1 : 1

2

25 : 1

3

5 : 1

4

3 : 2

Explanation:

Intensity ratio $= \frac{(a + b)^{2}}{(a - b)^{2}}$
$∴$ Intensity ratio $= {(\frac{r + 1}{r - 1})}^{2}$
$= {(\frac{\frac{3}{2} + 1}{\frac{3}{2} - 1})}^{2}$
Intensity ratio $= 25 : 1$ .

PHXII10:WAVE OPTICS

368067 The ratio of intensities at two points $P$ and $Q$ on the screen in a Young's double slit experiment where phase difference between two waves of same amplitude are $π / 3$ and $π / 2$ , respectively are

1

3 : 1

2

3 : 2

3

1 : 3

4

3 : 1

Explanation:

Resultant intensity, $I_{net} = I_{1} + I_{2} + 2 \sqrt{I_{1} I_{2}} \cos ϕ$
where $ϕ =$ phase difference.
$I_{1} = I_{0} + I_{0} + 2 I_{0} \cos \frac{π}{3}$ for $(ϕ = \frac{π}{3})$
$I_{1} = 2 I_{0} + 2 I_{0} \times \frac{1}{2} = 3 I_{0}$ $I_{2} = I_{0} + I_{0} + 2 I_{0} \cos \frac{π}{2} = 2 I_{0}$ for $(ϕ = \frac{π}{2})$
Hence, ratio between the two waves
$= \frac{I_{1}}{I_{2}} = \frac{3}{2} \frac{I_{0}}{I_{0}} = \frac{3}{2}$

JEE - 2023

PHXII10:WAVE OPTICS

368064 For sustained interference fringes in double slit experiment, essential conditions /is /are
(a) Sources must be coherent
(b) The intensities of the two sources must be equal.
Here, the correct option / s / is / are

1

b o t h a, b

2 only

a

3 only

b

4 neither

a

nor

b

PHXII10:WAVE OPTICS

368065 In a Young’s double slit experiment, the separation of the two slits is doubled. To keep the same spacing of fringes, the distance $D$ of the screen from the slits should be made

1

\frac{D}{2}

2

\frac{D}{\sqrt{2}}

3

2 D

4

4 D

Explanation:

$β = β^{'} o r \frac{D λ}{d} = \frac{D^{'} λ}{(2 d)} ∴ D^{'} = 2 D$

PHXII10:WAVE OPTICS

368066 The width of two slits in young's experiment are in the ratio of $9 : 4$ . What will be the intensity ratio of maxima and minima in the interference pattern?

1

1 : 1

2

25 : 1

3

5 : 1

4

3 : 2

Explanation:

Intensity ratio $= \frac{(a + b)^{2}}{(a - b)^{2}}$
$∴$ Intensity ratio $= {(\frac{r + 1}{r - 1})}^{2}$
$= {(\frac{\frac{3}{2} + 1}{\frac{3}{2} - 1})}^{2}$
Intensity ratio $= 25 : 1$ .

PHXII10:WAVE OPTICS

368067 The ratio of intensities at two points $P$ and $Q$ on the screen in a Young's double slit experiment where phase difference between two waves of same amplitude are $π / 3$ and $π / 2$ , respectively are

1

3 : 1

2

3 : 2

3

1 : 3

4

3 : 1

Explanation:

Resultant intensity, $I_{net} = I_{1} + I_{2} + 2 \sqrt{I_{1} I_{2}} \cos ϕ$
where $ϕ =$ phase difference.
$I_{1} = I_{0} + I_{0} + 2 I_{0} \cos \frac{π}{3}$ for $(ϕ = \frac{π}{3})$
$I_{1} = 2 I_{0} + 2 I_{0} \times \frac{1}{2} = 3 I_{0}$ $I_{2} = I_{0} + I_{0} + 2 I_{0} \cos \frac{π}{2} = 2 I_{0}$ for $(ϕ = \frac{π}{2})$
Hence, ratio between the two waves
$= \frac{I_{1}}{I_{2}} = \frac{3}{2} \frac{I_{0}}{I_{0}} = \frac{3}{2}$

JEE - 2023

PHXII10:WAVE OPTICS

368064 For sustained interference fringes in double slit experiment, essential conditions /is /are
(a) Sources must be coherent
(b) The intensities of the two sources must be equal.
Here, the correct option / s / is / are

1

b o t h a, b

2 only

a

3 only

b

4 neither

a

nor

b

PHXII10:WAVE OPTICS

368065 In a Young’s double slit experiment, the separation of the two slits is doubled. To keep the same spacing of fringes, the distance $D$ of the screen from the slits should be made

1

\frac{D}{2}

2

\frac{D}{\sqrt{2}}

3

2 D

4

4 D

Explanation:

$β = β^{'} o r \frac{D λ}{d} = \frac{D^{'} λ}{(2 d)} ∴ D^{'} = 2 D$

PHXII10:WAVE OPTICS

368066 The width of two slits in young's experiment are in the ratio of $9 : 4$ . What will be the intensity ratio of maxima and minima in the interference pattern?

1

1 : 1

2

25 : 1

3

5 : 1

4

3 : 2

Explanation:

Intensity ratio $= \frac{(a + b)^{2}}{(a - b)^{2}}$
$∴$ Intensity ratio $= {(\frac{r + 1}{r - 1})}^{2}$
$= {(\frac{\frac{3}{2} + 1}{\frac{3}{2} - 1})}^{2}$
Intensity ratio $= 25 : 1$ .

PHXII10:WAVE OPTICS

368067 The ratio of intensities at two points $P$ and $Q$ on the screen in a Young's double slit experiment where phase difference between two waves of same amplitude are $π / 3$ and $π / 2$ , respectively are

1

3 : 1

2

3 : 2

3

1 : 3

4

3 : 1

Explanation:

Resultant intensity, $I_{net} = I_{1} + I_{2} + 2 \sqrt{I_{1} I_{2}} \cos ϕ$
where $ϕ =$ phase difference.
$I_{1} = I_{0} + I_{0} + 2 I_{0} \cos \frac{π}{3}$ for $(ϕ = \frac{π}{3})$
$I_{1} = 2 I_{0} + 2 I_{0} \times \frac{1}{2} = 3 I_{0}$ $I_{2} = I_{0} + I_{0} + 2 I_{0} \cos \frac{π}{2} = 2 I_{0}$ for $(ϕ = \frac{π}{2})$
Hence, ratio between the two waves
$= \frac{I_{1}}{I_{2}} = \frac{3}{2} \frac{I_{0}}{I_{0}} = \frac{3}{2}$

JEE - 2023

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