An object 15cm high is placed 10cm from the optical center of a thin lens. Its image is formed 25cm from the optical center on the same side of the lens as the object

Options

A. 2.5cm
B. 0.2cm
C. 16.7cm
D. 37.5cm

Explanation

To solve the problem step by step, we will use the lens formula and the magnification formula.

### Given:
- Height of the object (h) = 15 cm
- Object distance (u) = -10 cm (negative because the object is on the same side as the incoming light)
- Image distance (v) = -25 cm (negative because the image is formed on the same side as the object)

### Step 1: Understand the Sign Convention
In optics, we use a sign convention where:
- Distances measured against the direction of incident light are negative.
- Distances measured in the direction of incident light are positive.

### Step 2: Use the Magnification Formula
The magnification (m) of a lens is given by the formula:
\[ m = \frac{h'}{h} = \frac{v}{u} \]
where:
- \( h' \) = height of the image
- \( h \) = height of the object
- \( v \) = image distance
- \( u \) = object distance

### Step 3: Substitute the Values
We can rearrange the magnification formula to find the height of the image:
\[ h' = m \cdot h \]
Substituting the values:
\[ m = \frac{v}{u} = \frac{-25}{-10} = 2.5 \]

Now, substituting this back into the height formula:
\[ h' = 2.5 \cdot 15 \]

### Step 4: Calculate the Height of the Image
\[ h' = 37.5 \text{ cm} \]

### Conclusion
The height of the image is 37.5 cm.

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