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PHXII10:WAVE OPTICS

367993 When a thin transparent plate of thickness t and refractive index $μ$ is placed in the path of one of the two interfering waves of light, then the path difference changes by

1

(μ + 1) t

2

\frac{(μ + 1)}{t}

3

\frac{(μ - 1)}{t}

4

(μ - 1) t

Explanation:

Optical path length in vacuum $= t$
Optical path length in the medium $= μ t$
Path difference $= t (μ - 1)$
NOTE: Here all lengths are measured w.r.to vacuum.

PHXII10:WAVE OPTICS

367994 When a mica sheet of thickness 7 microns and $μ = 1.6$ is placed in the path of one of interfering beams in the biprism experiment then the central fringe gets at the position of seventh bright fringe. The wavelength of light used will be

1

4000

A^{\circ}

2

5000

A^{\circ}

3

6000

A^{\circ}

4

7000

A^{\circ}

Explanation:

$λ = \frac{(μ - 1) t}{n} (1)$
According to question
$n = 7. μ = 1.6, t = 7 \times 10^{- 6} (2)$ meter
From eqs. (1) and (2), $λ = 6 \times 10^{- 7}$ meter
$i . e ., 6000$ $A^{\circ}$ $(1$ $A^{\circ}$ $= 10^{- 10} m)$

PHXII10:WAVE OPTICS

367995 Assertion :
The pattern and the position of fringes always remain same even after the introduction of transparent medium in a path of one of the slit.
Reason :
The central fringe is bright or dark depends upon the initial phase difference between the two coherent sources.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

AIIMS - 2012

PHXII10:WAVE OPTICS

367996 Two transparent slabs are placed infront of two slits in $Y D S E$ . The path difference between $S_{1} P a n d S_{2} P$ is
supporting img

1

\frac{y d}{D} + t_{2} (μ_{2} - 1)

2

t_{2} (μ_{2} - μ_{1})

3

\frac{y D}{d}

4

[\frac{y d}{D} + t_{2} (μ_{2} - 1)] - [t_{1} (μ_{1} - 1)]

Explanation:

Path length of ray $1 = (S_{1} P - t_{1}) + t_{1} μ_{1}$
Path length of ray $2 = (S_{2} P - t_{2}) + t_{2} μ_{2}$
Path difference
$= [S_{2} P - t_{2} + μ_{2} t_{2}] - [(S_{1} P - t_{1}) + μ_{1} t_{1}]$
$= [(S_{2} P - S_{1} P) + t_{2} (μ_{2} - 1)] - t_{1} (μ_{1} - 1)$
$= [d \sin θ + t_{2} (μ_{2} - 1)] - t_{1} (μ_{1} - 1)$
$= [\frac{y d}{D} + t_{2} (μ_{2} - 1)] - t_{1} (μ_{1} - 1)$

PHXII10:WAVE OPTICS

367993 When a thin transparent plate of thickness t and refractive index $μ$ is placed in the path of one of the two interfering waves of light, then the path difference changes by

1

(μ + 1) t

2

\frac{(μ + 1)}{t}

3

\frac{(μ - 1)}{t}

4

(μ - 1) t

Explanation:

Optical path length in vacuum $= t$
Optical path length in the medium $= μ t$
Path difference $= t (μ - 1)$
NOTE: Here all lengths are measured w.r.to vacuum.

PHXII10:WAVE OPTICS

367994 When a mica sheet of thickness 7 microns and $μ = 1.6$ is placed in the path of one of interfering beams in the biprism experiment then the central fringe gets at the position of seventh bright fringe. The wavelength of light used will be

1

4000

A^{\circ}

2

5000

A^{\circ}

3

6000

A^{\circ}

4

7000

A^{\circ}

Explanation:

$λ = \frac{(μ - 1) t}{n} (1)$
According to question
$n = 7. μ = 1.6, t = 7 \times 10^{- 6} (2)$ meter
From eqs. (1) and (2), $λ = 6 \times 10^{- 7}$ meter
$i . e ., 6000$ $A^{\circ}$ $(1$ $A^{\circ}$ $= 10^{- 10} m)$

PHXII10:WAVE OPTICS

367995 Assertion :
The pattern and the position of fringes always remain same even after the introduction of transparent medium in a path of one of the slit.
Reason :
The central fringe is bright or dark depends upon the initial phase difference between the two coherent sources.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

AIIMS - 2012

PHXII10:WAVE OPTICS

367996 Two transparent slabs are placed infront of two slits in $Y D S E$ . The path difference between $S_{1} P a n d S_{2} P$ is
supporting img

1

\frac{y d}{D} + t_{2} (μ_{2} - 1)

2

t_{2} (μ_{2} - μ_{1})

3

\frac{y D}{d}

4

[\frac{y d}{D} + t_{2} (μ_{2} - 1)] - [t_{1} (μ_{1} - 1)]

Explanation:

Path length of ray $1 = (S_{1} P - t_{1}) + t_{1} μ_{1}$
Path length of ray $2 = (S_{2} P - t_{2}) + t_{2} μ_{2}$
Path difference
$= [S_{2} P - t_{2} + μ_{2} t_{2}] - [(S_{1} P - t_{1}) + μ_{1} t_{1}]$
$= [(S_{2} P - S_{1} P) + t_{2} (μ_{2} - 1)] - t_{1} (μ_{1} - 1)$
$= [d \sin θ + t_{2} (μ_{2} - 1)] - t_{1} (μ_{1} - 1)$
$= [\frac{y d}{D} + t_{2} (μ_{2} - 1)] - t_{1} (μ_{1} - 1)$

PHXII10:WAVE OPTICS

367993 When a thin transparent plate of thickness t and refractive index $μ$ is placed in the path of one of the two interfering waves of light, then the path difference changes by

1

(μ + 1) t

2

\frac{(μ + 1)}{t}

3

\frac{(μ - 1)}{t}

4

(μ - 1) t

Explanation:

Optical path length in vacuum $= t$
Optical path length in the medium $= μ t$
Path difference $= t (μ - 1)$
NOTE: Here all lengths are measured w.r.to vacuum.

PHXII10:WAVE OPTICS

367994 When a mica sheet of thickness 7 microns and $μ = 1.6$ is placed in the path of one of interfering beams in the biprism experiment then the central fringe gets at the position of seventh bright fringe. The wavelength of light used will be

1

4000

A^{\circ}

2

5000

A^{\circ}

3

6000

A^{\circ}

4

7000

A^{\circ}

Explanation:

$λ = \frac{(μ - 1) t}{n} (1)$
According to question
$n = 7. μ = 1.6, t = 7 \times 10^{- 6} (2)$ meter
From eqs. (1) and (2), $λ = 6 \times 10^{- 7}$ meter
$i . e ., 6000$ $A^{\circ}$ $(1$ $A^{\circ}$ $= 10^{- 10} m)$

PHXII10:WAVE OPTICS

367995 Assertion :
The pattern and the position of fringes always remain same even after the introduction of transparent medium in a path of one of the slit.
Reason :
The central fringe is bright or dark depends upon the initial phase difference between the two coherent sources.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

AIIMS - 2012

PHXII10:WAVE OPTICS

367996 Two transparent slabs are placed infront of two slits in $Y D S E$ . The path difference between $S_{1} P a n d S_{2} P$ is
supporting img

1

\frac{y d}{D} + t_{2} (μ_{2} - 1)

2

t_{2} (μ_{2} - μ_{1})

3

\frac{y D}{d}

4

[\frac{y d}{D} + t_{2} (μ_{2} - 1)] - [t_{1} (μ_{1} - 1)]

Explanation:

Path length of ray $1 = (S_{1} P - t_{1}) + t_{1} μ_{1}$
Path length of ray $2 = (S_{2} P - t_{2}) + t_{2} μ_{2}$
Path difference
$= [S_{2} P - t_{2} + μ_{2} t_{2}] - [(S_{1} P - t_{1}) + μ_{1} t_{1}]$
$= [(S_{2} P - S_{1} P) + t_{2} (μ_{2} - 1)] - t_{1} (μ_{1} - 1)$
$= [d \sin θ + t_{2} (μ_{2} - 1)] - t_{1} (μ_{1} - 1)$
$= [\frac{y d}{D} + t_{2} (μ_{2} - 1)] - t_{1} (μ_{1} - 1)$

PHXII10:WAVE OPTICS

367993 When a thin transparent plate of thickness t and refractive index $μ$ is placed in the path of one of the two interfering waves of light, then the path difference changes by

1

(μ + 1) t

2

\frac{(μ + 1)}{t}

3

\frac{(μ - 1)}{t}

4

(μ - 1) t

Explanation:

Optical path length in vacuum $= t$
Optical path length in the medium $= μ t$
Path difference $= t (μ - 1)$
NOTE: Here all lengths are measured w.r.to vacuum.

PHXII10:WAVE OPTICS

367994 When a mica sheet of thickness 7 microns and $μ = 1.6$ is placed in the path of one of interfering beams in the biprism experiment then the central fringe gets at the position of seventh bright fringe. The wavelength of light used will be

1

4000

A^{\circ}

2

5000

A^{\circ}

3

6000

A^{\circ}

4

7000

A^{\circ}

Explanation:

$λ = \frac{(μ - 1) t}{n} (1)$
According to question
$n = 7. μ = 1.6, t = 7 \times 10^{- 6} (2)$ meter
From eqs. (1) and (2), $λ = 6 \times 10^{- 7}$ meter
$i . e ., 6000$ $A^{\circ}$ $(1$ $A^{\circ}$ $= 10^{- 10} m)$

PHXII10:WAVE OPTICS

367995 Assertion :
The pattern and the position of fringes always remain same even after the introduction of transparent medium in a path of one of the slit.
Reason :
The central fringe is bright or dark depends upon the initial phase difference between the two coherent sources.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

AIIMS - 2012

PHXII10:WAVE OPTICS

367996 Two transparent slabs are placed infront of two slits in $Y D S E$ . The path difference between $S_{1} P a n d S_{2} P$ is
supporting img

1

\frac{y d}{D} + t_{2} (μ_{2} - 1)

2

t_{2} (μ_{2} - μ_{1})

3

\frac{y D}{d}

4

[\frac{y d}{D} + t_{2} (μ_{2} - 1)] - [t_{1} (μ_{1} - 1)]

Explanation:

Path length of ray $1 = (S_{1} P - t_{1}) + t_{1} μ_{1}$
Path length of ray $2 = (S_{2} P - t_{2}) + t_{2} μ_{2}$
Path difference
$= [S_{2} P - t_{2} + μ_{2} t_{2}] - [(S_{1} P - t_{1}) + μ_{1} t_{1}]$
$= [(S_{2} P - S_{1} P) + t_{2} (μ_{2} - 1)] - t_{1} (μ_{1} - 1)$
$= [d \sin θ + t_{2} (μ_{2} - 1)] - t_{1} (μ_{1} - 1)$
$= [\frac{y d}{D} + t_{2} (μ_{2} - 1)] - t_{1} (μ_{1} - 1)$

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