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

Options

A. a)
B. b)
C. c)
D. d) None of the options

Answer

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

### Step-by-step Solution:

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.

2. **Rearrange the Formula**:
We need to rearrange this equation to express \( \frac{1}{v} \) in terms of \( \frac{1}{u} \):
\[ \frac{1}{v} = -\frac{1}{u} + \frac{1}{f} \]

3. **Identify the Form of the Equation**:
The equation \( \frac{1}{v} = -\frac{1}{u} + \frac{1}{f} \) can be compared to the slope-intercept form of a straight line, \( y = mx + c \):
- Here, \( y = \frac{1}{v} \)
- \( x = \frac{1}{u} \)
- The slope \( m = -1 \) (indicating a negative slope)
- The y-intercept \( c = \frac{1}{f} \)

4. **Graph Characteristics**:
Since the slope is negative, the graph will be a straight line that decreases as \( \frac{1}{u} \) increases. The line will intersect the y-axis at \( \frac{1}{f} \).

5. **Analyze the Options**:
Given the options, we need to identify which graph corresponds to a straight line with a negative slope and a y-intercept at \( \frac{1}{f} \).

6. **Conclusion**:
After analyzing the options, we find that the correct graph is the one that shows a straight line with a negative slope and an intercept at \( \frac{1}{f} \). Therefore, the correct answer is option **B**.