For sperical mirros graph plotted between `- (1)/(V)` and `-(1)/(u)is` .

Options

A. stright line with slope 1
B. straight line with slope -1
C. Parabola
D. none

Answer

To solve the problem of plotting the graph between \(-\frac{1}{V}\) and \(-\frac{1}{u}\) for spherical mirrors, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Mirror Formula**:
The mirror formula for spherical mirrors 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.

2. **Rearranging the Equation**:
We can rearrange the mirror formula to express it in terms of \(-\frac{1}{V}\) and \(-\frac{1}{u}\):
\[ \frac{1}{v} = \frac{1}{f} - \frac{1}{u} \]
Multiplying the entire equation by \(-1\):
\[ -\frac{1}{v} = -\frac{1}{f} + \frac{1}{u} \]
This can be rewritten as:
\[ -\frac{1}{v} + \frac{1}{u} = -\frac{1}{f} \]

3. **Substituting Variables**:
Let:
\[ X = -\frac{1}{v} \quad \text{and} \quad Y = -\frac{1}{u} \]
Therefore, we can rewrite the equation as:
\[ X + Y = -\frac{1}{f} \]

4. **Identifying the Equation of a Line**:
The equation \(X + Y = -\frac{1}{f}\) can be rearranged to:
\[ Y = -X - \frac{1}{f} \]
This is in the form of \(Y = mX + c\), where \(m\) is the slope and \(c\) is the y-intercept.

5. **Determining the Slope**:
From the equation \(Y = -X - \frac{1}{f}\), we can see that the slope \(m = -1\).

6. **Conclusion**:
Since the graph of \(-\frac{1}{V}\) versus \(-\frac{1}{u}\) is a straight line with a slope of \(-1\), the correct answer to the question is that the graph is a straight line with a slope of \(-1\).

### Final Answer:
The graph plotted between \(-\frac{1}{V}\) and \(-\frac{1}{u}\) is a straight line with a slope of \(-1\).

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