Question:
In Young's double-slit experiment, the fringe width is proportional to
In Young's double-slit experiment, the fringe width is proportional to
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Remember, in Young's double-slit experiment, the fringe width is directly proportional to the wavelength of light used and inversely proportional to the separation between the slits.
Updated On: May 31, 2026
- $\lambda$
- $1/\lambda$
- $d$
- $1/D$
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The Correct Option is A
Solution and Explanation
Step 1: Concept
In Young's double-slit experiment, the fringe width (\(\Delta y\)) is a measure of the distance between adjacent bright or dark fringes on the screen. The formula for the fringe width in this context is given by: \[\Delta y = \frac{\lambda D}{d}\] where \(\lambda\) is the wavelength of light, \(D\) is the distance from the slits to the screen, and \(d\) is the separation between the two slits.
Step 2: Meaning
The fringe width depends on the wavelength of the light used in the experiment, the distance from the slits to the observation screen, and the separation between the two slits. The relationship indicates that if any one of these factors changes, it will affect the fringe width proportionally.
Step 3: Analysis
To determine which factor is proportional to the fringe width, we analyze the formula: \[\Delta y = \frac{\lambda D}{d}\] If \(\lambda\) (wavelength) increases, \(\Delta y\) also increases. If \(D\) (distance from slits to screen) increases, \(\Delta y\) increases. If \(d\) (slit separation) increases, \(\Delta y\) decreases. From the options provided: A) \(\lambda\): As discussed, an increase in wavelength leads to an increase in fringe width. B) \(1/\lambda\): This would imply that as the wavelength decreases, the fringe width increases. However, from the formula, it is clear that a decrease in \(\lambda\) results in a decrease in \(\Delta y\). C) \(d\): An increase in slit separation leads to a decrease in fringe width. D) \(1/D\): This would imply that as the distance from slits to screen decreases, the fringe width increases. However, from the formula, it is clear that a decrease in \(D\) results in a decrease in \(\Delta y\).
Step 4: Conclusion
The only factor among the options provided that directly affects the fringe width in proportionality is the wavelength of light (\(\lambda\)). Final Answer: (A)
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