In displacement method, convex lens forms a real image of an object for its two different positions. If heights of the images in two cases be 24 cm and 6 cm, then the height of the object is

Options

A. 3 cm
B. 36 cm
C. 6 cm
D. 12 cm

Answer

To find the height of the object using the displacement method, we can use the relationship between the heights of the images formed by the convex lens at two different positions.

### Step-by-Step Solution:

1. **Identify Given Values**:
- Height of the first image, \( h_1 = 24 \, \text{cm} \)
- Height of the second image, \( h_2 = 6 \, \text{cm} \)

2. **Use the Formula**:
The height of the object \( h_o \) can be calculated using the formula:
\[ h_o = \sqrt{h_1 \times h_2} \]
where \( h_1 \) and \( h_2 \) are the heights of the images formed by the lens.

3. **Substitute the Values**:
Substitute the values of \( h_1 \) and \( h_2 \) into the formula:
\[ h_o = \sqrt{24 \times 6} \]

4. **Calculate the Product**:
Calculate the product inside the square root:
\[ 24 \times 6 = 144 \]

5. **Calculate the Square Root**:
Now, take the square root of 144:
\[ h_o = \sqrt{144} = 12 \, \text{cm} \]

6. **Conclusion**:
The height of the object is \( h_o = 12 \, \text{cm} \).

### Final Answer:
The height of the object is \( 12 \, \text{cm} \).

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