Find distanace of image from a convex lens of focal length
`20cm` if object is placed at a distance of `30cm` from the lens. Also find its
magnification.

Explanation

To solve the problem of finding the distance of the image from a convex lens and the magnification, we can follow these steps:

### Step 1: Identify the given values
- Focal length of the lens (F) = +20 cm (positive for convex lens)
- Object distance (u) = -30 cm (negative as per sign convention)

### Step 2: Use the lens formula
The lens formula is given by:
\[ \frac{1}{F} = \frac{1}{V} - \frac{1}{U} \]
We need to find the image distance (V).

### Step 3: Substitute the values into the lens formula
Substituting the known values into the formula:
\[ \frac{1}{20} = \frac{1}{V} - \frac{1}{-30} \]
This simplifies to:
\[ \frac{1}{20} = \frac{1}{V} + \frac{1}{30} \]

### Step 4: Rearrange the equation to find V
Rearranging gives:
\[ \frac{1}{V} = \frac{1}{20} - \frac{1}{30} \]

### Step 5: Find a common denominator and simplify
The least common multiple (LCM) of 20 and 30 is 60. Therefore, we can rewrite the fractions:
\[ \frac{1}{20} = \frac{3}{60}, \quad \frac{1}{30} = \frac{2}{60} \]
Substituting these values back:
\[ \frac{1}{V} = \frac{3}{60} - \frac{2}{60} = \frac{1}{60} \]

### Step 6: Solve for V
Taking the reciprocal gives:
\[ V = 60 \text{ cm} \]

### Step 7: Determine the nature of the image
Since V is positive, the image is formed on the opposite side of the lens from the object, indicating that it is a real image.

### Step 8: Calculate the magnification (M)
The magnification is given by the formula:
\[ M = \frac{V}{U} \]
Substituting the values:
\[ M = \frac{60}{-30} = -2 \]

### Step 9: Interpret the magnification
The negative sign indicates that the image is inverted, and the magnitude of 2 indicates that the image is twice the size of the object.

### Final Results
- Distance of the image from the lens (V) = **60 cm**
- Magnification (M) = **-2** (indicating a real, inverted image that is 2 times larger than the object)

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