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If a light source more than 20 ft away comes to a focus 20 cm behind the lens, calculate the power of the lens.

 To calculate the power of the lens, you can use the lens formula, which relates the focal length (f) of a lens to the object distance (u) and the image distance (v) from the lens.

 

The lens formula is given by:

 

1/f = 1/v - 1/u

 

Where:

f = focal length of the lens (in meters)

v = image distance (in meters)

u = object distance (in meters)

 

In this case, the object distance (u) is the distance of the light source from the lens, which is more than 20 feet away. We need to convert this distance to meters.

 

1 foot is approximately 0.3048 meters.

 

So, the object distance (u) in meters would be:

 

u = 20 feet * 0.3048 meters/foot = 6.096 meters

 

The image distance (v) is given as 20 cm, which needs to be converted to meters:

 

v = 20 cm * 0.01 meters/cm = 0.2 meters

 

Now, we can calculate the focal length (f) using the lens formula:

 

1/f = 1/v - 1/u

1/f = 1/0.2 - 1/6.096

1/f = 5 - 0.16404

1/f = 4.83596

 

Now, find the reciprocal to get the value of f:

 

f = 1 / 4.83596 ≈ 0.2068 meters

 

Finally, to get the power of the lens, use the formula:

 

Power (P) = 1 / f

 

P = 1 / 0.2068 ≈ 4.839 Diopters

 

The power of the lens is approximately +4.839 Diopters. Note that the power is positive, indicating that the lens is a converging lens (a lens that brings light rays to a focus).

 

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