The graph between `(1)/(v)` and `(1)/(u)` for a concave mirror looks like.

Options

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Answer

To determine the graph between \(\frac{1}{v}\) and \(\frac{1}{u}\) for a concave mirror, we can follow these steps:

### Step 1: Understand the Mirror Formula
The mirror formula for a concave mirror is given by:
\[ \frac{1}{f} = \frac{1}{v} + \frac{1}{u} \]
where \(f\) is the focal length, \(v\) is the image distance, and \(u\) is the object distance.

### Step 2: Rearrange the Mirror Formula
We want to plot a graph between \(\frac{1}{v}\) and \(\frac{1}{u}\). Rearranging the mirror formula gives us:
\[ \frac{1}{v} = -\frac{1}{u} + \frac{1}{f} \]
This equation can be rewritten in the form of \(y = mx + c\):
- Here, \(y\) is \(\frac{1}{v}\),
- \(x\) is \(\frac{1}{u}\),
- The slope \(m\) is \(-1\),
- The y-intercept \(c\) is \(\frac{1}{f}\).

### Step 3: Analyze the Graph
From the rearranged formula:
- The slope is negative, indicating that as \(\frac{1}{u}\) increases, \(\frac{1}{v}\) decreases.
- The y-intercept is a constant value \(\frac{1}{f}\), which is specific to the concave mirror and does not change.

### Step 4: Identify the Type of Graph
Since the relationship is linear (as indicated by the form \(y = mx + c\)), we can conclude that the graph is a straight line with:
- A negative slope,
- A definite y-intercept.

### Step 5: Conclusion
Based on the analysis, the graph between \(\frac{1}{v}\) and \(\frac{1}{u}\) for a concave mirror is a straight line with a negative slope and a positive y-intercept.

### Final Answer
The graph between \(\frac{1}{v}\) and \(\frac{1}{u}\) for a concave mirror is a straight line with a negative slope and a positive y-intercept.

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