The minimum distance she can hold the coin from the lens is the sum of the focal length of the lens and the diameter of the coin.

The diameter of a US quarter is 0.955 inches.

The diameter of a US dime is 0.705 inches.

The diameter of a US penny is 0.717 inches.

Her focal length is about 4 inches.

The diameter of a quarter is 0.955 + 4 = 4.955 inches.

The diameter of a dime is 0.705 + 4 = 4.705 inches.

The diameter of a penny is 0.717 + 4 = 4.717 inches.

That is the closest she can hold the coin to the lens and have it appear in focus.

## How Far Away from the Lens Can She Place the Coin to have it Appear in Focus?

The maximum distance she can hold the coin away from the lens is the diameter of the coin divided by the focal length of the lens.

The diameter of a US quarter is 0.955 inches.

The diameter of a US dime is 0.705 inches.

The diameter of a US penny is 0.717 inches.

Her focal length is about 4 inches.

The diameter of a quarter is 0.955 / 4 = 0.236 inches.

The diameter of a dime is 0.705 / 4 = 0.171 inches.

The diameter of a penny is 0.717 / 4 = 0.201 inches.

That is the farthest she can hold the coin away from the lens and have it appear in focus.

## What are the Distances that she can Hold the Coin to have it Appear in Focus?

She can hold the coin in from the lens at 0.236 inches to have it appear in focus.

She can hold the coin from the lens at 0.171 inches to have it appear in focus.

She can hold the coin from the lens at 0.201 inches to have it appear in focus.

How Far Away from the Lens Can she Place the Coin to have it Appear in Focus?

She can place the coin at 0.236 inches from the lens to have it appear in focus.

She can place the coin at 0.171 inches from the lens to have it appear in focus.

She can place the coin at 0.201 inches from the lens to have it appear in focus.

## Conclusion

To have a coin appear in focus she must hold it from 0.236 inches to 0.201 inches away from the lens.

The furthest possible distance is 0.955 inches.

The closest possible distance is 0.717 inches.

If she wants to hold the coin in focus at the same distance, the diameter of the coin will be different.