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.

how to solve

To determine the powers needed for the prescription bifocals, we can use the concept of lens power and the relationship between focal length and object distance.

Let's start with the distant objects. The woman can see clearly when objects are between 45 cm and 155 cm away with her right eye. Since the glasses will be 2 cm from the eye, we can consider the effective object distance to be the distance from the glasses to the eye. So, we need to find a lens power that will focus the distant object at around 155 cm.

Using the formula:

Lens Power (in Diopters) = 1 / Focal Length (in meters)

We can calculate the focal length required for distant objects:

Focal Length = 155 cm = 1.55 meters

Lens Power for distant objects = 1 / 1.55 = 0.645 Diopters

Now, let's move on to reading a book. The woman wants to read a book at 25 cm away. Again, considering the glasses will be 2 cm from the eye, the effective object distance will be the distance from the glasses to the eye plus the reading distance. Therefore, we need to find a lens power that will focus the book at around 27 cm (2 cm + 25 cm).

Focal Length = 27 cm = 0.27 meters

Lens Power for reading = 1 / 0.27 = 3.704 Diopters

So, the prescription bifocals should have a power of approximately 0.645 Diopters for the upper part (for distant objects) and 3.704 Diopters for the lower part (for reading a book).

It's important to note that these calculations provide approximate values. A professional optometrist should be consulted for an accurate prescription and fitting.