Distance of an object from a concave lens of focal length 20 cm is 40 cm. Then linear magnification of the image

Options

A. 1
B. `lt1`
C. `lt1`
D. zero

Explanation

To find the linear magnification of the image formed by a concave lens, we can follow these steps:

### Step 1: Identify the given values
- Focal length of the concave lens (f) = -20 cm (negative because it is a concave lens)
- Object distance (u) = -40 cm (negative as per the sign convention for lenses)

### Step 2: Use the lens formula
The lens formula is given by:
\[ \frac{1}{v} - \frac{1}{u} = \frac{1}{f} \]
Rearranging this gives:
\[ \frac{1}{v} = \frac{1}{f} + \frac{1}{u} \]

### Step 3: Substitute the values into the lens formula
Substituting the values of f and u into the lens formula:
\[ \frac{1}{v} = \frac{1}{-20} + \frac{1}{-40} \]

### Step 4: Find a common denominator and simplify
The common denominator for -20 and -40 is -40. Thus:
\[ \frac{1}{v} = \frac{-2}{40} + \frac{-1}{40} = \frac{-3}{40} \]

### Step 5: Solve for v
Taking the reciprocal gives:
\[ v = \frac{-40}{3} \text{ cm} \]

### Step 6: Calculate the magnification (m)
The magnification (m) is given by the formula:
\[ m = \frac{v}{u} \]
Substituting the values of v and u:
\[ m = \frac{-40/3}{-40} = \frac{1}{3} \]

### Step 7: Conclusion
The linear magnification of the image is:
\[ m = \frac{1}{3} \]
This means the image is smaller than the object.