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Chapter 18: Problem 85

If a graph is drawn between the separation of slits and bandwidth in Young's double slit experiment, the graph will be (A) a straight line having positive slope. (B) a straight line having negative slope. (C) a rectangular hyperbola. (D) a parabola.

Short Answer

Expert verified
The graph between the separation of slits (d) and bandwidth (尾) in Young's double slit experiment will be a rectangular hyperbola (option C) as the relationship is given by \(d * 尾 = 位L\), where 位L is a constant.

Step by step solution

01

Recall the formula for fringe width in Young's double slit experiment

The fringe width (bandwidth), denoted by '尾', of the interference pattern in Young's double-slit experiment is given by the formula: \[尾 = \frac{位L}{d}\] where: - 位 is the wavelength of the light used - L is the distance between the screen and the double slit - d is the separation between the slits
02

Rearrange the formula to express fringe width in terms of slit separation

Rearranging the formula from the previous step, we get: \[d = \frac{位L}{尾}\] This equation shows the relationship between the separation of slits (d) and bandwidth/ fringe width (尾).
03

Determine the type of graph

Comparing the equation we derived to standard equations of graphs, it's evident that it resembles the equation of a rectangular hyperbola: \[xy = k\] In our case, we have \(d * 尾 = 位L\), where 位L is a constant (for a given wavelength and setup). So, the graph between the separation of slits (d) and bandwidth (尾) will be a rectangular hyperbola. Therefore, the correct answer is option (C).

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