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: Write 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 of the mirror,
- \(v\) is the image distance,
- \(u\) is the object distance.

### Step 2: Rearrange the Mirror Formula
We can rearrange the mirror formula to express \(\frac{1}{v}\) in terms of \(\frac{1}{u}\):
\[ \frac{1}{v} = \frac{1}{f} - \frac{1}{u} \]
This can be rewritten as:
\[ \frac{1}{v} = -\frac{1}{u} + \frac{1}{f} \]

### Step 3: Identify the Form of the Equation
The equation \(\frac{1}{v} = -\frac{1}{u} + \frac{1}{f}\) is in the form of \(y = mx + c\), where:
- \(y = \frac{1}{v}\),
- \(x = \frac{1}{u}\),
- The slope \(m = -1\),
- The y-intercept \(c = \frac{1}{f}\).

### Step 4: Graph the Equation
From the equation, we can see that the graph will be a straight line with:
- A negative slope (indicating that as \(\frac{1}{u}\) increases, \(\frac{1}{v}\) decreases),
- A y-intercept at \(\frac{1}{f}\).

### Step 5: Conclusion
Thus, the graph between \(\frac{1}{v}\) and \(\frac{1}{u}\) for a concave mirror will be a straight line that slopes downwards from left to right, intersecting the y-axis at \(\frac{1}{f}\).

### Final Answer
The graph is a straight line with a negative slope, indicating the relationship between \(\frac{1}{v}\) and \(\frac{1}{u}\) for a concave mirror.

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