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?
Question
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?
Solution
To solve this problem, we need to use the lens formula and magnification formula.
- Lens formula: 1/f = 1/v - 1/u
- 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.
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