A convex lens of focal length 20 cm, forms a real image of double the size of the object. The object distance is

Given: A convex lens of focal length 20cm forms a real image that is double the size of the object. We need to find the object distance (u).

Step-by-Step Solution

1. For a convex lens of focal length 20cm, the magnification (m) is given as -2. Since the image is real and inverted, the magnification is negative.
2. The magnification formula for a lens is: 
   m = v / u   where v is the image distance, and u is the object distance.
3. Rearranging this formula, we get: 
   v = m * u
4. Substituting m = -2, we have: 
   v = -2 * u
5. The lens formula is: 
   (1/f) = (1/v) - (1/u)   where f is the focal length of the convex lens.
6. Substituting f = 20 cm and v = -2u into the lens formula: 
   (1/20) = (1/(-2u)) - (1/u)
7. Simplifying the equation: 
   (1/20) = (-1/(2u)) - (1/u)
8. Combine the terms on the right-hand side: 
   (1/20) = (-1 - 2) / (2u) 
(1/20) = -3 / (2u)
9. Cross-multiply to solve for u: 
   2u = -3 * 20 
u = -30 cm

Final Answer

The object distance is -30 cm, which means the object is placed 30 cm in front of the convex lens of focal length 20cm.