Question 264: Waves Optics

Question

In Young's double slit experiment with monochromatic light of wavelength 600 nm , the distance between the slits is $10^{-3} \mathrm{~m}$. For changing the fringe width by $3 	imes 10^{-5} \mathrm{~m}$
a. the screen is moved away from the slit by 5 cm .
b. the screen is moved 5 cm towards the slits.
c. the screen is moved 3 cm towards the slits.
d. the screen is moved away from the slits by 3 cm .

Accepted Answer

In Young's double slit experiment, the fringe width $(\beta)$ is given by:
$$ \beta = \frac{\lambda D}{d} $$
where
$\lambda =$ wavelength of light = $600\ \mathrm{nm} = 600 	imes 10^{-9}\ \mathrm{m}$
$D =$ distance between slits and screen
$d =$ separation between the slits = $10^{-3}\ \mathrm{m}$
Let the initial fringe width be $\beta_1$ at distance $D_1$, and the new fringe width be $\beta_2$ at distance $D_2$.
Given,
$$ \beta_2 - \beta_1 = 3 	imes 10^{-5}\ \mathrm{m} $$
So,
$$ \beta_2 = \frac{\lambda D_2}{d} $$
$$ \beta_1 = \frac{\lambda D_1}{d} $$
Therefore,
$$ \beta_2 - \beta_1 = \frac{\lambda}{d} (D_2 - D_1) = 3 	imes 10^{-5}\ \mathrm{m} $$
Substituting the values:
$$ \lambda = 600 	imes 10^{-9}\ \mathrm{m} $$
$$ d = 10^{-3}\ \mathrm{m} $$
So,
$$ \frac{600 	imes 10^{-9}}{10^{-3}} (D_2 - D_1) = 3 	imes 10^{-5} $$
Simplifying:
$$ (600 	imes 10^{-6})(D_2 - D_1) = 3 	imes 10^{-5} $$
$$ D_2 - D_1 = \frac{3 	imes 10^{-5}}{600 	imes 10^{-6}} $$
$$ D_2 - D_1 = \frac{3 	imes 10^{-5}}{6 	imes 10^{-4}} $$
$$ D_2 - D_1 = \frac{3}{6} 	imes \frac{10^{-5}}{10^{-4}} $$
$$ D_2 - D_1 = \frac{1}{2} 	imes 0.1 $$
$$ D_2 - D_1 = 0.05\ \mathrm{m} $$
$$ D_2 - D_1 = 5\ \mathrm{cm} $$
This means the
distance between the screen and slits must change by $5$ cm
to change the fringe width by $3 	imes 10^{-5}\ \mathrm{m}$.
If $D_2 > D_1$
, the screen is moved
away
from the slits by 5 cm.
If $D_2 < D_1$
, the screen is moved
towards
the slits by 5 cm.
Correct options according to the question:
The screen is moved away by $5\ \mathrm{cm}$ (
option a
).
The screen is moved $5\ \mathrm{cm}$ towards the slits (
option b
).
So, the correct answer is:
Option B: both (a) and (b)

Answer

both (c) and (d)

Answer

both (a) and (b)

Answer

only (a)

Answer

only (c)

Waves Optics

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