QBManager

WAVE OPTICS

283389 Two sources give interference pattern which is observed on a screen, placed at a distance $D$ from the sources. The fringe width is given as 2 W. If the distance of sources from the screen is doubled, then the fringe width will

1 become

W / 2

2 remains the same

3 become

W

4 become

4 W

Explanation:

: The fringe width is given in interference pattern
$W = \frac{λ D}{d}$
Case-I
Given, $W_{1} = 2 W \Rightarrow 2 W = \frac{λ D}{d}$
Case-II
Given, $D^{'} = 2 D$
$W_{2} = \frac{λ D^{'}}{d} = \frac{2 λ D}{d}$
$= 2 \times 2 W$
$= 4 W$

Manipal UGET-2016

WAVE OPTICS

283392 In a double slit experiment, $5^{th}$ dark fringe is formed opposite to one of the slits the wavelength of light is

1

\frac{d^{2}}{6 D}

2

\frac{d^{2}}{5 D}

3

\frac{d^{2}}{15 D}

4

\frac{d^{2}}{9 D}

Explanation:

: In young's double slit experiment position of $n^{th}$ dark fringes is given by,
$x_{n} = \frac{D}{d} (2 n - 1) \frac{λ}{2}$
$λ = \frac{2 x_{n} d}{D (2 n - 1)}$
$5^{th}$ dark fringes is formed opposite to one of the slit,
$2 x_{5} = d$
$x_{5} = \frac{d}{2}$
From equation (i), we get-
$λ = \frac{2 x_{5} d}{D (2 \times 5 - 1)} = \frac{d \times d}{9 D}$
$(∵ x_{5} = \frac{d}{2})$
$= \frac{d^{2}}{9 D}$

MHT-CET 2019

WAVE OPTICS

283393 In Young's double slit experiment, the spacing between the slits is $d$ and wavelength of light used is $6000 \AA$ . If the angular width of a fringe formed on a distance screen is $1^{\circ}$ , then value of $d$ is

1

1 mm

2

0.05 mm

3

0.03 mm

4

0.01 mm

Explanation:

: Given,
$λ = 6000 \AA = 6 \times 10^{- 7} m$
$θ = 1^{\circ} = \frac{π}{180^{\circ}} rad$
Spacing between the slits,
$d = \frac{λ}{θ}$
$d = \frac{6 \times 10^{- 7}}{π / 180^{\circ}}$
$d = 34.39 \times 10^{- 6} m$
$d = 0.034 mm$

VITEEE-2010

WAVE OPTICS

283394 Four light sources produce the following four waves:
(i) $y_{1} = a \sin (ω t + ϕ_{1})$
(ii) $y_{2} = a \sin 2 ω t$
(iii) $y_{3} = a \sin (ω t + ϕ_{2})$
(iv) $y_{4} = a \sin (3 ω t + ϕ)$
Superposition of which two waves give rise to interference?

1 (i) and (ii)

2 (ii) and (iii)

3 (i) and (iii)

4 (iii) and (iv)

Explanation:

: Interference takes place between two waves having equal frequency and propagate in same direction.
Hence, $y_{1} = a \sin (ω t + ϕ)$
$y_{3} = a^{'} \sin (ω t + ϕ)$
We know that, $ω = 2 π f$
or
$f = \frac{ω}{2 π}$
$\frac{ω_{1}}{2 π} = \frac{ω_{2}}{2 π}$
$ω_{1} = ω_{2}$ Hence, it is clear from the expression that to get sustained interference between two waves source it must propagate in same direction and have equal frequency.

VITEEE-2009

WAVE OPTICS

283389 Two sources give interference pattern which is observed on a screen, placed at a distance $D$ from the sources. The fringe width is given as 2 W. If the distance of sources from the screen is doubled, then the fringe width will

1 become

W / 2

2 remains the same

3 become

W

4 become

4 W

Explanation:

: The fringe width is given in interference pattern
$W = \frac{λ D}{d}$
Case-I
Given, $W_{1} = 2 W \Rightarrow 2 W = \frac{λ D}{d}$
Case-II
Given, $D^{'} = 2 D$
$W_{2} = \frac{λ D^{'}}{d} = \frac{2 λ D}{d}$
$= 2 \times 2 W$
$= 4 W$

Manipal UGET-2016

WAVE OPTICS

283392 In a double slit experiment, $5^{th}$ dark fringe is formed opposite to one of the slits the wavelength of light is

1

\frac{d^{2}}{6 D}

2

\frac{d^{2}}{5 D}

3

\frac{d^{2}}{15 D}

4

\frac{d^{2}}{9 D}

Explanation:

: In young's double slit experiment position of $n^{th}$ dark fringes is given by,
$x_{n} = \frac{D}{d} (2 n - 1) \frac{λ}{2}$
$λ = \frac{2 x_{n} d}{D (2 n - 1)}$
$5^{th}$ dark fringes is formed opposite to one of the slit,
$2 x_{5} = d$
$x_{5} = \frac{d}{2}$
From equation (i), we get-
$λ = \frac{2 x_{5} d}{D (2 \times 5 - 1)} = \frac{d \times d}{9 D}$
$(∵ x_{5} = \frac{d}{2})$
$= \frac{d^{2}}{9 D}$

MHT-CET 2019

WAVE OPTICS

283393 In Young's double slit experiment, the spacing between the slits is $d$ and wavelength of light used is $6000 \AA$ . If the angular width of a fringe formed on a distance screen is $1^{\circ}$ , then value of $d$ is

1

1 mm

2

0.05 mm

3

0.03 mm

4

0.01 mm

Explanation:

: Given,
$λ = 6000 \AA = 6 \times 10^{- 7} m$
$θ = 1^{\circ} = \frac{π}{180^{\circ}} rad$
Spacing between the slits,
$d = \frac{λ}{θ}$
$d = \frac{6 \times 10^{- 7}}{π / 180^{\circ}}$
$d = 34.39 \times 10^{- 6} m$
$d = 0.034 mm$

VITEEE-2010

WAVE OPTICS

283394 Four light sources produce the following four waves:
(i) $y_{1} = a \sin (ω t + ϕ_{1})$
(ii) $y_{2} = a \sin 2 ω t$
(iii) $y_{3} = a \sin (ω t + ϕ_{2})$
(iv) $y_{4} = a \sin (3 ω t + ϕ)$
Superposition of which two waves give rise to interference?

1 (i) and (ii)

2 (ii) and (iii)

3 (i) and (iii)

4 (iii) and (iv)

Explanation:

: Interference takes place between two waves having equal frequency and propagate in same direction.
Hence, $y_{1} = a \sin (ω t + ϕ)$
$y_{3} = a^{'} \sin (ω t + ϕ)$
We know that, $ω = 2 π f$
or
$f = \frac{ω}{2 π}$
$\frac{ω_{1}}{2 π} = \frac{ω_{2}}{2 π}$
$ω_{1} = ω_{2}$ Hence, it is clear from the expression that to get sustained interference between two waves source it must propagate in same direction and have equal frequency.

VITEEE-2009

WAVE OPTICS

283389 Two sources give interference pattern which is observed on a screen, placed at a distance $D$ from the sources. The fringe width is given as 2 W. If the distance of sources from the screen is doubled, then the fringe width will

1 become

W / 2

2 remains the same

3 become

W

4 become

4 W

Explanation:

: The fringe width is given in interference pattern
$W = \frac{λ D}{d}$
Case-I
Given, $W_{1} = 2 W \Rightarrow 2 W = \frac{λ D}{d}$
Case-II
Given, $D^{'} = 2 D$
$W_{2} = \frac{λ D^{'}}{d} = \frac{2 λ D}{d}$
$= 2 \times 2 W$
$= 4 W$

Manipal UGET-2016

WAVE OPTICS

283392 In a double slit experiment, $5^{th}$ dark fringe is formed opposite to one of the slits the wavelength of light is

1

\frac{d^{2}}{6 D}

2

\frac{d^{2}}{5 D}

3

\frac{d^{2}}{15 D}

4

\frac{d^{2}}{9 D}

Explanation:

: In young's double slit experiment position of $n^{th}$ dark fringes is given by,
$x_{n} = \frac{D}{d} (2 n - 1) \frac{λ}{2}$
$λ = \frac{2 x_{n} d}{D (2 n - 1)}$
$5^{th}$ dark fringes is formed opposite to one of the slit,
$2 x_{5} = d$
$x_{5} = \frac{d}{2}$
From equation (i), we get-
$λ = \frac{2 x_{5} d}{D (2 \times 5 - 1)} = \frac{d \times d}{9 D}$
$(∵ x_{5} = \frac{d}{2})$
$= \frac{d^{2}}{9 D}$

MHT-CET 2019

WAVE OPTICS

283393 In Young's double slit experiment, the spacing between the slits is $d$ and wavelength of light used is $6000 \AA$ . If the angular width of a fringe formed on a distance screen is $1^{\circ}$ , then value of $d$ is

1

1 mm

2

0.05 mm

3

0.03 mm

4

0.01 mm

Explanation:

: Given,
$λ = 6000 \AA = 6 \times 10^{- 7} m$
$θ = 1^{\circ} = \frac{π}{180^{\circ}} rad$
Spacing between the slits,
$d = \frac{λ}{θ}$
$d = \frac{6 \times 10^{- 7}}{π / 180^{\circ}}$
$d = 34.39 \times 10^{- 6} m$
$d = 0.034 mm$

VITEEE-2010

WAVE OPTICS

283394 Four light sources produce the following four waves:
(i) $y_{1} = a \sin (ω t + ϕ_{1})$
(ii) $y_{2} = a \sin 2 ω t$
(iii) $y_{3} = a \sin (ω t + ϕ_{2})$
(iv) $y_{4} = a \sin (3 ω t + ϕ)$
Superposition of which two waves give rise to interference?

1 (i) and (ii)

2 (ii) and (iii)

3 (i) and (iii)

4 (iii) and (iv)

Explanation:

: Interference takes place between two waves having equal frequency and propagate in same direction.
Hence, $y_{1} = a \sin (ω t + ϕ)$
$y_{3} = a^{'} \sin (ω t + ϕ)$
We know that, $ω = 2 π f$
or
$f = \frac{ω}{2 π}$
$\frac{ω_{1}}{2 π} = \frac{ω_{2}}{2 π}$
$ω_{1} = ω_{2}$ Hence, it is clear from the expression that to get sustained interference between two waves source it must propagate in same direction and have equal frequency.

VITEEE-2009

WAVE OPTICS

283389 Two sources give interference pattern which is observed on a screen, placed at a distance $D$ from the sources. The fringe width is given as 2 W. If the distance of sources from the screen is doubled, then the fringe width will

1 become

W / 2

2 remains the same

3 become

W

4 become

4 W

Explanation:

: The fringe width is given in interference pattern
$W = \frac{λ D}{d}$
Case-I
Given, $W_{1} = 2 W \Rightarrow 2 W = \frac{λ D}{d}$
Case-II
Given, $D^{'} = 2 D$
$W_{2} = \frac{λ D^{'}}{d} = \frac{2 λ D}{d}$
$= 2 \times 2 W$
$= 4 W$

Manipal UGET-2016

WAVE OPTICS

283392 In a double slit experiment, $5^{th}$ dark fringe is formed opposite to one of the slits the wavelength of light is

1

\frac{d^{2}}{6 D}

2

\frac{d^{2}}{5 D}

3

\frac{d^{2}}{15 D}

4

\frac{d^{2}}{9 D}

Explanation:

: In young's double slit experiment position of $n^{th}$ dark fringes is given by,
$x_{n} = \frac{D}{d} (2 n - 1) \frac{λ}{2}$
$λ = \frac{2 x_{n} d}{D (2 n - 1)}$
$5^{th}$ dark fringes is formed opposite to one of the slit,
$2 x_{5} = d$
$x_{5} = \frac{d}{2}$
From equation (i), we get-
$λ = \frac{2 x_{5} d}{D (2 \times 5 - 1)} = \frac{d \times d}{9 D}$
$(∵ x_{5} = \frac{d}{2})$
$= \frac{d^{2}}{9 D}$

MHT-CET 2019

WAVE OPTICS

283393 In Young's double slit experiment, the spacing between the slits is $d$ and wavelength of light used is $6000 \AA$ . If the angular width of a fringe formed on a distance screen is $1^{\circ}$ , then value of $d$ is

1

1 mm

2

0.05 mm

3

0.03 mm

4

0.01 mm

Explanation:

: Given,
$λ = 6000 \AA = 6 \times 10^{- 7} m$
$θ = 1^{\circ} = \frac{π}{180^{\circ}} rad$
Spacing between the slits,
$d = \frac{λ}{θ}$
$d = \frac{6 \times 10^{- 7}}{π / 180^{\circ}}$
$d = 34.39 \times 10^{- 6} m$
$d = 0.034 mm$

VITEEE-2010

WAVE OPTICS

283394 Four light sources produce the following four waves:
(i) $y_{1} = a \sin (ω t + ϕ_{1})$
(ii) $y_{2} = a \sin 2 ω t$
(iii) $y_{3} = a \sin (ω t + ϕ_{2})$
(iv) $y_{4} = a \sin (3 ω t + ϕ)$
Superposition of which two waves give rise to interference?

1 (i) and (ii)

2 (ii) and (iii)

3 (i) and (iii)

4 (iii) and (iv)

Explanation:

: Interference takes place between two waves having equal frequency and propagate in same direction.
Hence, $y_{1} = a \sin (ω t + ϕ)$
$y_{3} = a^{'} \sin (ω t + ϕ)$
We know that, $ω = 2 π f$
or
$f = \frac{ω}{2 π}$
$\frac{ω_{1}}{2 π} = \frac{ω_{2}}{2 π}$
$ω_{1} = ω_{2}$ Hence, it is clear from the expression that to get sustained interference between two waves source it must propagate in same direction and have equal frequency.

VITEEE-2009