Question 7: Wave Optics

Question

Assertion :
If a glass slab is placed in front of
one of the slits, then fringe with will
decrease.
Reason :
Glass slab will produce an
additional path difference.

Accepted Answer

To determine the correct answer, let's analyze both the
Assertion
and the
Reason
separately.
Assertion:
"If a glass slab is placed in front of one of the slits, then fringe width will decrease."
Analysis:
In a Young's double-slit experiment, the
fringe width ($ \beta $)
is given by the formula:
$ \beta = \frac{\lambda D}{d} $
Where:
$ \lambda $ is the wavelength of the light used.
$ D $ is the distance between the slits and the screen.
$ d $ is the distance between the two slits.
When a
glass slab
of thickness $ t $ and refractive index $ \mu $ is placed in front of one of the slits, it introduces an
additional optical path difference ($ \Delta $)
given by:
$ \Delta = (\mu - 1) t $
Effects of the Glass Slab:
Shift of Fringe Pattern:
The additional path difference causes the entire interference pattern to shift
laterally
but
does not alter the fringe width
.
Fringe Width Remains Unchanged:
The fringe width $ \beta $ depends only on $ \lambda $, $ D $, and $ d $, none of which are affected by the introduction of the glass slab.
Conclusion on Assertion:
The assertion claims that the fringe width will
decrease
, which is
incorrect
.
The fringe width remains
constant
; only the position of the fringes shifts.
Reason:
"Glass slab will produce an additional path difference."
Analysis:
The glass slab increases the optical path length for the light passing through it.
This introduces an
additional path difference ($ \Delta $)
between the two interfering waves.
The calculation for the additional path difference is:
$   \Delta = (\mu - 1) t   $
Conclusion on Reason:
The reason correctly states that the glass slab produces an additional path difference.
This is a
true statement
.
Final Conclusion:
Assertion:
Incorrect
The fringe width does
not decrease
when a glass slab is placed in front of one slit.
Reason:
Correct
The glass slab does produce an additional path difference, causing a shift in the interference pattern.
Relation Between Assertion and Reason:
The reason is
correct
, but it does
not explain
the (incorrect) assertion.
Answer:
Option D
Assertion is incorrect and Reason is correct.

Answer

Both Assertion and Reason are correct, Reason is the correct explanation of Assertion

Answer

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

Answer

Assertion is correct and Reason is incorrect

Answer

Assertion is incorrect and Reason is correct

Wave Optics

Assertion : If a glass slab is placed in front of one of the slits, then fringe with will decrease. Reason : Glass slab will produce an additional path difference.

Choose the correct answer: