A person struggles to read by holding a book at arms length, a distance of 50.0 cm. What power of reading glasses should be prescribed for him, assuming they will be placed 2.0 cm from the eye and he wanted to read at normal near point of 25.0 cm?
To determine the power of reading glasses needed, we can use the lens formula:
1/f = 1/v - 1/u,
Where:
- f is the focal length of the lens,
- v is the image distance,
- u is the object distance.
In this case, the person's near point is considered as the object distance (u), which is 25.0 cm, and the glasses will be placed 2.0 cm from the eye. Hence, the image distance (v) is 2.0 cm.
Now, let's substitute the given values into the lens formula to find the focal length (f):
1/f = 1/2.0 - 1/25.0.
To simplify the equation, we need to find a common denominator:
1/f = (25 - 2) / (2 * 25)
= 23 / 50.
Now, let's invert both sides of the equation to find f:
f = 50 / 23
≈ 2.17 cm.
The focal length of the lens required for the reading glasses is approximately 2.17 cm.
To convert the focal length (f) to power (P), we use the equation:
P = 1/f.
Substituting the value of f:
P = 1/2.17
≈ 0.46 diopters.
Therefore, the power of reading glasses that should be prescribed for the person is approximately +0.46 diopters.