For statement of question 118, if the heights of the two images are `h_(1)` and `h_(2)` , respectively,then the height of the object (h) is

Options

A. `h_(1)+h_(2)`
B. `h_(1)h_(2)`
C. `sqrt(h_(1)h_(2))`
D. `h_(1)//h_(2)`

Explanation

To find the height of the object (h) given the heights of the two images (h1 and h2), we can use the concept of magnification in optics. Here's a step-by-step solution:

### Step 1: Understand the relationship between magnification and image height
The magnification (M) produced by a lens is defined as the ratio of the height of the image (h) to the height of the object (H). Therefore, we can express the magnifications for the two images as:
- For the first image: \( M_1 = \frac{h_1}{h} \)
- For the second image: \( M_2 = \frac{h_2}{h} \)

### Step 2: Use the property of magnification
According to the problem, when two images are formed on the same screen by changing the position of the lens, the product of the magnifications is equal to 1:
\[ M_1 \times M_2 = 1 \]

### Step 3: Substitute the magnifications into the equation
Substituting the expressions for \( M_1 \) and \( M_2 \):
\[ \left(\frac{h_1}{h}\right) \times \left(\frac{h_2}{h}\right) = 1 \]

### Step 4: Simplify the equation
This simplifies to:
\[ \frac{h_1 \times h_2}{h^2} = 1 \]

### Step 5: Rearrange to find the height of the object
Cross-multiplying gives:
\[ h_1 \times h_2 = h^2 \]

### Step 6: Solve for the height of the object
Taking the square root of both sides:
\[ h = \sqrt{h_1 \times h_2} \]

### Conclusion
Thus, the height of the object (h) is given by:
\[ h = \sqrt{h_1 \times h_2} \]

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