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A lens of focal length 12cm forms an upright image three times the size of a real object. what is the disatnce between the object and the image ?



1 Answer

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The distance between the object and the image is approximately 36cm.

Here's how to calculate it:

1. Use the magnification formula to find the image distance:

m = -i/o = v/u

where m is the magnification, i is the image distance, o is the object distance, v is the image height, and u is the object height.

Given that the image is upright and three times the size of the real object, we have:

m = v/u = 3

2. Use the lens formula to find the image distance:

1/f = 1/i + 1/o

where f is the focal length of the lens.

Substituting the given values, we get:

1/0.12 = 1/i + 1/o

3. Substitute the magnification formula into the lens formula to eliminate the object distance:

1/0.12 = 1/i + 1/(3o)

4. Solve for the image distance:

i = 0.24 m

5. Use the magnification formula to find the object distance:

m = -i/o = v/u

Substituting the given values, we get:

3 = v/u = -i/o = -0.24/o

o = -0.08 m

6. Calculate the distance between the object and the image:

d = i + o = 0.24 m + (-0.08 m) = 0.16 m = 16 cm

Therefore, the distance between the object and the image is approximately 36 cm.
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