Introduction:
A convex lens is a type of lens that is thicker in the middle and thinner at the edges. It is commonly referred to as a converging lens because it converges or brings parallel rays of light together at a specific point called the focal point. The focal length of a lens is the distance between the lens and its focal point. In this scenario, the convex lens has a focal length of 20 cm and it produces a magnification of 2 when an object is placed in front of it.

Explanation:
- Definition of magnification: Magnification is the ratio of the size of an image to the size of the object. It tells us how much larger or smaller the image appears compared to the object. In this case, the magnification is given as 2, which means the image formed by the lens is twice the size of the object.
- Calculation of magnification: The formula for magnification is given as:
Magnification = (Image height / Object height) = (Image distance / Object distance)
In this case, the magnification is given as 2. Let's assume the object height and distance as 'h' and 'd' respectively, and the image height and distance as 'h' and 'd' respectively. So, we have:
2 = (h / h) = (d' / d)
Since h / h is equal to 1, the magnification equation simplifies to:
2 = (d' / d)
This implies that the image distance is twice the object distance.
- Relationship between object distance and image distance: According to the lens formula, the relationship between the object distance (u), image distance (v), and focal length (f) of a lens is given as:
1 / f = 1 / v - 1 / u
In this case, the focal length is given as 20 cm. We can rearrange the lens formula to solve for the image distance:
1 / v = 1 / f + 1 / u
Plugging in the values, we get:
1 / v = 1 / 20 + 1 / u
Since v is twice the value of u, we can substitute 2u for v:
1 / (2u) = 1 / 20 + 1 / u
Solving this equation, we find that u = 20 cm and v = 40 cm.
- Conclusion: Therefore, when an object is placed in front of a convex lens with a focal length of 20 cm, the image distance is 40 cm, and the image formed is twice the size of the object.