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In Young's double-slit experiment, the w...

In Young's double-slit experiment, the wavelength of light was changed from `7000 Å` to 3500 Å`. While doubling the separation between the slits, which of the following is not true for this experiment?

A

The width of fringe changes.

B

The color of bright fringes change.

C

The separation between seccessive bright fringes changes.

D

The separation between successive bright fringes unchanged.

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The correct Answer is:
To solve the problem, we need to analyze the effects of changing the wavelength of light and the separation between the slits in Young's double-slit experiment. ### Step-by-Step Solution: 1. **Understand the Fringe Width Formula**: The fringe width (β) in Young's double-slit experiment is given by the formula: \[ \beta = \frac{\lambda D}{d} \] where: - \(\lambda\) = wavelength of light - \(D\) = distance from the slits to the screen - \(d\) = separation between the slits 2. **Initial Conditions**: Initially, the wavelength is \(\lambda = 7000 \, \text{Å}\) and the separation between the slits is \(d\). 3. **Change in Wavelength**: The wavelength is changed to \(\lambda' = 3500 \, \text{Å}\). This means: \[ \lambda' = \frac{\lambda}{2} \] 4. **Doubling the Slit Separation**: The separation between the slits is doubled, so: \[ d' = 2d \] 5. **Calculate New Fringe Width**: The new fringe width (β') can be calculated using the new values: \[ \beta' = \frac{\lambda' D}{d'} = \frac{\left(\frac{\lambda}{2}\right) D}{2d} = \frac{\lambda D}{4d} = \frac{\beta}{4} \] This shows that the new fringe width is one-fourth of the original fringe width. 6. **Analyze Each Option**: - **Option A**: "The width of fringe changes." - This is true since the new fringe width is \(\frac{\beta}{4}\). - **Option B**: "The color of bright fringes changes." - This is also true because the wavelength has changed, affecting the color. - **Option C**: "The separation between the successive bright fringes changes." - This is true as the fringe width has changed, which directly affects the separation of bright fringes. 7. **Conclusion**: Since all the options A, B, and C are true, we need to identify which statement is "not true". However, based on the analysis, all statements are true. Therefore, the question may have a misunderstanding or misinterpretation. ### Final Answer: None of the options provided are false based on the analysis. All options are true.

To solve the problem, we need to analyze the effects of changing the wavelength of light and the separation between the slits in Young's double-slit experiment. ### Step-by-Step Solution: 1. **Understand the Fringe Width Formula**: The fringe width (β) in Young's double-slit experiment is given by the formula: \[ \beta = \frac{\lambda D}{d} ...
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