Where must an object be placed in front of a convex lens of focal length 20cm toobtain a real and four times magnified image? Where will the image be formed?

To solve this problem, we need to use the lens formula and magnification formula.

1. Lens formula: 1/f = 1/v - 1/u
2. Magnification formula: m = -v/u

Given:

• Focal length (f) = 20 cm
• Magnification (m) = -4 (It's negative because the image is real and inverted)

First, let's use the magnification formula to find the object distance (u).

m = -v/u => -4 = -v/u => v = 4u

Now, substitute v = 4u into the lens formula:

1/f = 1/v - 1/u => 1/20 = 1/(4u) - 1/u => 1/20 = (1 - 4) / 4u => 1/20 = -3/4u => u = -80/3 cm

So, the object must be placed approximately 26.67 cm in front of the lens.

Now, substitute u = -80/3 cm into the equation v = 4u to find the image distance (v):

v = 4u => v = 4 * -80/3 => v = -320/3 cm

So, the image will be formed approximately 106.67 cm in front of the lens.