If an object is placed 10 cm in front of a concave mirror of focal length 20cm, the image will be

Options

A. Diminished, upright, virtual
B. Enlarged, upright, virtual
C. Diminished, inverted, real
D. Enlarged, upright, real

Answer

To solve the problem of finding the characteristics of the image formed by a concave mirror when an object is placed 10 cm in front of it, we will use the mirror formula and the magnification formula. Here are the steps to arrive at the solution:

### Step 1: Identify the given values
- Focal length of the concave mirror (f) = -20 cm (negative because it is a concave mirror)
- Object distance (u) = -10 cm (negative according to the sign convention, as the object is in front of the mirror)

### Step 2: Use the mirror formula
The mirror formula is given by:
\[ \frac{1}{f} = \frac{1}{u} + \frac{1}{v} \]
Where:
- \( f \) = focal length
- \( u \) = object distance
- \( v \) = image distance

### Step 3: Substitute the known values into the mirror formula
Substituting \( f = -20 \) cm and \( u = -10 \) cm into the formula:
\[ \frac{1}{-20} = \frac{1}{-10} + \frac{1}{v} \]

### Step 4: Solve for \( \frac{1}{v} \)
Rearranging the equation gives:
\[ \frac{1}{v} = \frac{1}{-20} - \frac{1}{-10} \]
Calculating the right side:
\[ \frac{1}{v} = -\frac{1}{20} + \frac{1}{10} \]
Finding a common denominator (20):
\[ \frac{1}{v} = -\frac{1}{20} + \frac{2}{20} = \frac{1}{20} \]

### Step 5: Calculate \( v \)
Taking the reciprocal gives:
\[ v = 20 \text{ cm} \]

### Step 6: Determine the nature of the image
Since \( v \) is positive, the image is formed on the same side as the object, indicating that the image is virtual.

### Step 7: Calculate the magnification
The magnification (m) is given by:
\[ m = -\frac{v}{u} \]
Substituting the values:
\[ m = -\frac{20}{-10} = 2 \]

### Step 8: Analyze the magnification
A magnification of 2 means that the image is twice the height of the object, indicating that it is enlarged. Since the magnification is positive, the image is upright.

### Conclusion
The characteristics of the image are:
- It is virtual
- It is upright
- It is enlarged

### Final Answer
The image will be virtual, upright, and enlarged.

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