An object is placed 25 cm in front of a concave lens of focal length 25 cm. The position of images is

Options

A. - 10 cm
B. + 10 cm
C. - 12 . 5 cm
D. 12 . 5 cm

Answer

To find the position of the image formed by a concave lens when an object is placed in front of it, we can use the lens formula:

### Step 1: Write down the lens formula
The lens formula is given by:
\[ \frac{1}{V} - \frac{1}{U} = \frac{1}{F} \]
where:
- \( V \) = image distance from the lens
- \( U \) = object distance from the lens
- \( F \) = focal length of the lens

### Step 2: Identify the values
In this case:
- The focal length \( F \) of the concave lens is -25 cm (negative because it is a concave lens).
- The object distance \( U \) is -25 cm (negative because the object is placed in front of the lens).

### Step 3: Substitute the values into the lens formula
Substituting the values into the lens formula:
\[ \frac{1}{V} - \frac{1}{-25} = \frac{1}{-25} \]

### Step 4: Simplify the equation
Rearranging the equation gives:
\[ \frac{1}{V} + \frac{1}{25} = -\frac{1}{25} \]
\[ \frac{1}{V} = -\frac{1}{25} - \frac{1}{25} \]
\[ \frac{1}{V} = -\frac{2}{25} \]

### Step 5: Calculate the image distance \( V \)
Taking the reciprocal of both sides:
\[ V = -\frac{25}{2} \text{ cm} \]
This simplifies to:
\[ V = -12.5 \text{ cm} \]

### Step 6: Conclusion
The position of the image is at -12.5 cm from the lens, indicating that the image is formed on the same side as the object, which is typical for a concave lens.