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Intensity Explanation in YDSE

In a modified...

Question

In a modified $Y D S$ the two slits $S_{3}$ and $S_{4}$ are placed in front of the slits $S_{1}$ and $S_{2}$ ,calculate the ratio of $m a x^{m}$ intensity to minimum intensity produced in the screen if

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Solution

YDS
Two slits $S_{3}$ and $S_{4}$ are placed in front of slits $S_{1}$ and $S_{2}$
$\frac{I_{m a x}}{I_{m i n}} = \frac{(a_{1} + a_{2})^{2}}{(a_{1} - a_{2})^{2}}$
$a_{1}$ and $a_{2}$ be the amplitude of constructive and destructive mode.
In relation between intensity and amplitude
$I n t e n s i t y α (a m p l i t u d e)^{2}$

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Q. Consider the situation shown in the figure. The two slits S₁ and S₂ placed symmetrically around the central line are illuminated by a monochromatic light of wavelength λ. The separation between the slits is d. The light transmitted by the slits falls on a screen ∑₁ placed at a distance D from the slits. The slit S₃ is at the central line and the slit S₄ is at a distance z from S₃. Another screen ∑₂ is placed a further distance D away from ∑₁_. Find the ratio of the maximum to minimum intensity observed on ∑₂ if z is equal to
(a)

z = \frac{λ D}{2 d}

\frac{λ D}{d}

\frac{λ D}{4 d}

Q. In standard 'YDSE' (

D >> d >> λ

) with identical slits

S_{1}

S_{2}

, light reaching at point 'A' on the screen opposite to slit

S_{2}

has an intensity

I

. It was also found that when only one of the two slits

S_{1}

S_{2}

was illuminated by same light beam, the intensity at 'A' is still

I

. Now when a third slit

S_{3}

of four times the slit width(of

S_{1}

), is made as shown

(S_{1} S_{2} = S_{2} S_{3} = d)

and all the three slits are illuminated, then the intensity of light reaching 'A' is

n I

n

is (write upto two decimal places)

Y D S E

D >> d >> λ

) with identical slits

S_{1}

S_{2}

, light reaching at point

A

on the screen opposite to slit

S_{2}

has an intensity

I

. It was also found that when only one of the two slits

S_{1}

S_{2}

was illuminated by same light beam, the intensity at

A

I

. Now when a third slit

S_{3}

of four times the slit width(of

S_{1}

), is made as shown

(S_{1} S_{2} = S_{2} S_{3} = d)

and all the three slits are illuminated, then the intensity of light reaching

A

n I

n

Q. In a Young's double slit experiment, the slits

S_{1}

S_{2}

are illuminated by a parallel beam of light of wavelength

4000 ˙ A

from the medium of refractive index

μ_{1} = 1.2

. A thin film of thickness

1.2 μ m

and refractive index

μ = 1.5

is placed in front of

S_{1}

perpendicular to the path of light. The refractive index of the medium between the plane of slits and screen is

μ_{2} = 1.4

. If the light coming from

S_{1}

S_{2}

have equal intensity

I

, then the intensity at the geometrical centre of screen

O

Consider the situation shown in figure (17-E6). The two slits $S_{1}$ and $S_{2}$ placed symmetrically around the central line are illuminated by a monochromatic light of wavelength $λ$ the separation between the slits is d. The light transmitted by the slits falls on a screen $\sum_{1}$ placed at a distance D from the slits. The slit $S_{3}$ is at the central line and the slit $S_{4}$ is at a distane z rom $S_{3}$ Another screen $\sum_{2}$ is palced a further distance D away from $\sum_{1}$ find the ration of thmaximum to minimum intensity obsered on $\sum_{2}$ if z is equal to
(a) $z = \frac{λ D}{2 d}$
(b) $\frac{λ}{d},$
(c) $\frac{λ D}{4 d} .$

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