A point object is placed at a distamce of 10 cm anad its real image is formed at a distance of 20 cm from a concave mirror. If the object is moved by 0.1 cm towards the mirror. The image will shift by about

Options

A. 0.4 cm away form the mirror
B. 0.4 cm towards the mirror
C. 0.8 cm away from the mirror
D. 0.8cm towards the mirror

Explanation

To solve the problem step by step, we will use the mirror formula and the concept of magnification.

### Step 1: Identify the given values
- The object distance (u) = -10 cm (negative because it is in front of the mirror)
- The image distance (v) = -20 cm (negative because it is a real image formed on the same side as the object)

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

### Step 3: Determine the change in object distance (Δu)
The object is moved towards the mirror by 0.1 cm, so:
\[ \Delta u = -0.1 \, \text{cm} \]

### Step 4: Use the relationship between change in image distance (Δv) and change in object distance (Δu)
The relationship between the changes in image distance and object distance is given by:
\[ \frac{\Delta v}{\Delta u} = m^2 \]
Substituting the magnification:
\[ \frac{\Delta v}{\Delta u} = (-2)^2 = 4 \]

### Step 5: Calculate Δv
Now, we can find Δv:
\[ \Delta v = 4 \cdot \Delta u \]
Substituting Δu:
\[ \Delta v = 4 \cdot (-0.1) = -0.4 \, \text{cm} \]

### Step 6: Interpret the sign of Δv
Since Δv is negative, it indicates that the image shifts away from the mirror. Therefore, the image will shift by 0.4 cm away from the mirror.

### Final Answer
The image will shift by about **0.4 cm away from the mirror**.

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