The Question is from neet-physics , and it was created by the author ABDUL JILANI BASHA

Question

In Young's double-slit experiment, if the separation between the coherent sources is halved and the distance of the screen from the coherent sources is doubled, then the fringe width becomes:

ABDUL JILANI BASHA · Accepted Answer

## CORE INFORMATION
✓ **Answer**: Option D
## CONCEPT FRAMEWORK
 **Primary Concept**: Young's double-slit experiment and fringe width calculation
 **Related Topics**: Interference of light waves
 **Prerequisites**: Understanding of wave interference and basic trigonometry.
## SOLUTION PATHWAY
**Given Information**:
Initial separation between coherent sources: $d$
Initial distance of screen from sources: $D$
Fringe width is denoted by $β$
Separation between sources is halved: $d' = d/2$
Distance of screen is doubled: $D' = 2D$
**Method & Steps**:
1. **Formula for fringe width:** The fringe width ($β$) in Young's double-slit experiment is given by the formula:
	$β = \frac{λD}{d}$  where $λ$ is the wavelength of light.
2. **Calculate the new fringe width:**  Let's denote the new fringe width as $β'$.  Substituting the new values of $d$ and $D$ into the formula, we get:
	$β' = \frac{λD'}{d'} = \frac{λ(2D)}{d/2} = \frac{4λD}{d}$
3. **Compare the new and old fringe widths:** We can see that $β' = 4β$.
	Result: The new fringe width is four times the original fringe width.
	Verification: The calculation shows a direct proportionality between fringe width and distance to the screen, and an inverse proportionality to the slit separation. Doubling the distance and halving the separation results in a four-fold increase in fringe width.
 ## OPTION ANALYSIS
[A] :x: Halved: This would occur if the distance to the screen was halved and the separation was doubled.
[B] :x: Doubled: This would occur if either the distance was doubled or the separation was halved (but not both).
[C] :x: One-fourth: This would occur if the distance was halved and the separation was doubled.
[D] ✓: Four times: This is the correct answer, as demonstrated by the calculation.
 ## LEARNING AIDS
 **Common Mistakes**:
  1. Incorrectly applying the formula or mixing up the direct and inverse relationships between fringe width, slit separation, and screen distance: Pay close attention to the formula and the relationship between the variables.
  2. Forgetting to consider both changes simultaneously: It's essential to account for both the halving of the slit separation and the doubling of the screen distance.
 **Quick Tips**:
  1. Remember the formula $β = \frac{λD}{d}$ and analyze how each variable affects the fringe width.
  2. Use dimensional analysis to check if your answer makes sense.  The units of fringe width should remain consistent.

ABDUL JILANI BASHA · Answer

Halved

ABDUL JILANI BASHA · Answer

Doubled

ABDUL JILANI BASHA · Answer

One-fourth

ABDUL JILANI BASHA · Answer

The correct Option is "Four times"

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