A woman can see clearly her right eye only when objects are between 45 cm and 155 cm away. Prescription bifocals should have what powers so that she can see distant objects clearly(upper part) and be able to read a book 25 cm away(lower part) with her right eye? Assume that the glasses will be 2 cm from the eye.

Question

A woman can see clearly her right eye only when objects are between 45 cm and 155 cm away. Prescription bifocals should have what powers so that she can see distant objects clearly(upper part) and be able to read a book 25 cm away(lower part) with her right eye? Assume that the glasses will be 2 cm from the eye.

Answer 1

To determine the powers of the prescription bifocals for the woman's right eye, we need to consider the distance at which she can see clearly for both distant objects and reading a book.

Let's start with the upper part of the bifocals, which should correct her vision for distant objects. The glasses will be 2 cm from her eye, so we need to consider the distance from the glasses to the distant objects.

The woman can see clearly her right eye only when objects are between 45 cm and 155 cm away. Since the glasses will be 2 cm from her eye, we need to subtract the 2 cm to get the distance from the glasses. Therefore, the effective distance for the upper part of the bifocals will be between 43 cm (45 cm - 2 cm) and 153 cm (155 cm - 2 cm).

To calculate the power needed for the upper part, we can use the formula:

Power = 1/Distance

Let's convert the distances to meters:

Lower limit: 43 cm = 0.43 m
Upper limit: 153 cm = 1.53 m

Now we can calculate the powers:

Lower limit power for distant objects (upper part of bifocals) = 1/0.43 = 2.33 diopters (approximately)
Upper limit power for distant objects (upper part of bifocals) = 1/1.53 = 0.65 diopters (approximately)

Next, let's consider the lower part of the bifocals for reading a book at 25 cm. The glasses will be 2 cm from her eye, so the effective distance will be 23 cm (25 cm - 2 cm).

Using the same formula:

Power for reading the book (lower part of bifocals) = 1/0.23 = 4.35 diopters (approximately)

Therefore, the prescription bifocals for the woman's right eye should have approximately:
- A power of 2.33 diopters for the upper part to see distant objects clearly.
- A power of 4.35 diopters for the lower part to read a book at 25 cm.

It's important to note that this calculation assumes no astigmatism or other vision issues. It's always recommended to consult with an optometrist or ophthalmologist for an accurate prescription.