If the magnification of a virtual image formed by an object 10cm from a convex less is 3, then the focal length of the lens is

1. Analyze the question

We are given:

• Object distance ($u$) = $10\text{ cm}$
• Magnification ($m$) = $3$
• The image is virtual.
• We need to find the focal length ($f$) of the convex lens.

2. Explain the concept

For a lens, magnification ($m$) is defined as the ratio of the image distance ($v$) to the object distance ($u$):

Since the image is virtual, the image distance ($v$) must be treated as negative in the lens formula. The lens formula is:

3. Show the solution

Step 1: Find the image distance ($v$). Using the magnification formula:

Because the image is virtual, we assign a negative sign to $v$:

Step 2: Calculate the focal length ($f$) using the lens formula.

Find the common denominator (which is 30):

Therefore:

4. Identify the answer

The calculated focal length is $15\text{ cm}$, which matches option D.

5. Tip

Always remember the Sign Convention: For thin lenses, real images have a positive image distance ($v$), while virtual images have a negative image distance ($v$). If you forget this sign, you will likely get the wrong focal length!