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 find the distance of the image from a convex lens and the magnification, we can use the lens formula and the magnification formula.

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

### Step 2: Use the lens formula
The lens formula is given by:
\[ \frac{1}{v} - \frac{1}{u} = \frac{1}{f} \]
Substituting the known values into the formula:
\[ \frac{1}{v} - \frac{1}{-30} = \frac{1}{20} \]

### Step 3: Simplify the equation
Rearranging the equation gives:
\[ \frac{1}{v} + \frac{1}{30} = \frac{1}{20} \]
Now, we need a common denominator to combine the fractions. The least common multiple of 20 and 30 is 60. Thus, we rewrite the fractions:
\[ \frac{1}{v} + \frac{2}{60} = \frac{3}{60} \]
Subtract \(\frac{2}{60}\) from both sides:
\[ \frac{1}{v} = \frac{3}{60} - \frac{2}{60} = \frac{1}{60} \]

### Step 4: Solve for v
Taking the reciprocal gives:
\[ v = 60 \text{ cm} \]
This means the image is formed at a distance of 60 cm from the lens on the opposite side.

### Step 5: Calculate the magnification (m)
The magnification (m) is given by the formula:
\[ m = \frac{v}{u} \]
Substituting the values we have:
\[ m = \frac{60}{-30} = -2 \]

### Conclusion
- The distance of the image from the lens is **60 cm**.
- The magnification is **-2**, indicating that the image is real, inverted, and twice the size of the object.

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