1. First image formed by the lens

For the biconvex lens, $f=+15\text{ cm}$ Object distance from lens: $u=-30\text{ cm}$ (using Cartesian sign convention)

Lens formula: $\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$ So, $\frac{1}{15}=\frac{1}{v}-\left(-\frac{1}{30}\right)=\frac{1}{v}+\frac{1}{30}$ $\frac{1}{v}=\frac{1}{15}-\frac{1}{30}=\frac{1}{30}$ $v=+30\text{ cm}$

So the lens alone would form a real image 30 cm to the right of the lens.

2. Relation of this image with the plane mirror

The plane mirror is only $10\text{ cm}$ to the right of the lens. Hence the point where the lens would form image lies: $30-10=20\text{ cm}$ behind the mirror.

Thus, for the plane mirror, this acts as a virtual object at a distance $20\text{ cm}$ behind it.

A plane mirror forms the image as far behind/in front as the object is in front/behind. Therefore, the mirror forms an image 20 cm in front of the mirror.

Since the mirror is $10\text{ cm}$ to the right of the lens, this image is at: $10-20=-10\text{ cm}$ That is, 10 cm to the left of the lens.

This acts as the object for the lens during the return journey.

3. Second refraction through the lens

Now light is incident on the lens from the right side. The object for the lens is at $10\text{ cm}$ to the left of the lens. For this second pass, the object is on the opposite side from which light is coming, so it is a virtual object for the lens. Hence, $u=+10\text{ cm}$ For a convex lens, $f=+15\text{ cm}$

Using lens formula again: $\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$ $\frac{1}{15}=\frac{1}{v}-\frac{1}{10}$ $\frac{1}{v}=\frac{1}{15}+\frac{1}{10}=\frac{2+3}{30}=\frac{5}{30}=\frac{1}{6}$ $v=+6\text{ cm}$

Positive $v$ here means the final image is formed on the left side of the lens (the outgoing side for the returning rays), so the final image is real.

4. Distance of final image from the mirror

Mirror is $10\text{ cm}$ to the right of the lens. Final image is $6\text{ cm}$ to the left of the lens. So distance from mirror is: $10+6=16\text{ cm}$

5. Conclusion

The final image is:

• real
• 16 cm from the mirror

Therefore, the correct option is $\boxed{\text{B}}$