Question 78: Waves Optics

Question

In a Young's double slit experiment, the slits are separated by 0.2 mm . If the slits separation is increased to 0.4 mm , the percentage change of the fringe width is :

Accepted Answer

In Young's double slit experiment, the fringe width $$\beta$$ is given by:
$$\beta = \frac{\lambda D}{d}$$
where:
$$\lambda$$ is the wavelength of light,
$$D$$ is the distance from the slits to the screen,
$$d$$ is the separation between the slits.
Here's how the change affects the fringe width:
Initial Situation:
When $$d = 0.2 	ext{ mm}$$, the fringe width is:
$$\beta_{	ext{initial}} = \frac{\lambda D}{0.2 	ext{ mm}}$$
After Increasing Slit Separation:
When $$d$$ is increased to $$0.4 	ext{ mm}$$:
$$\beta_{	ext{new}} = \frac{\lambda D}{0.4 	ext{ mm}}$$
Comparing the Two Fringe Widths:
Notice that:
$$\beta_{	ext{new}} = \frac{1}{2} 	imes \frac{\lambda D}{0.2 	ext{ mm}} = \frac{1}{2} \beta_{	ext{initial}}$$
This means the fringe width is halved, which is a reduction of $$50\%$$.
Thus, the fringe width decreases by $$50\%$$ when the slit separation is increased from $$0.2 	ext{ mm}$$ to $$0.4 	ext{ mm}$$.
The correct answer is Option B: $$50\%$$.

Answer

$25 \%$

Answer

$50 \%$

Answer

$0 \%$

Answer

$100 \%$

Waves Optics

In a Young's double slit experiment, the slits are separated by 0.2 mm . If the slits separation is increased to 0.4 mm , the percentage change of the fringe width is :

Choose the correct answer: