# What is the power of the lens in diopters?

• KVM
In summary, the desired magnification for reading material is 3.5× when a book is placed 9.5 cm behind a lens. To find the power of the lens in diopters, the magnification was set equal to -di/do and solved for di, giving a value of -33.25 cm. When this value was plugged into the equation 1/f = 1/di + 1/do, the result was 0.075, which is not the correct answer. However, if the magnification is negative and di is positive, the equation will work out and f will be in meters, as required for the units of diopters.
KVM

## Homework Statement

It is desired to magnify reading material by a factor of 3.5× when a book is placed 9.5 cm behind a lens.
What is the power of the lens in diopters?

## Homework Equations

1/f = 1/di + 1/do
M = -di/do
P=1/f

## The Attempt at a Solution

I set equal the magnification to -di/do and solved for di
3.5=-di/9.5
di = -33.25 cm
Then I plugged into equation to find 1/f which = P
1/f = 1/di + 1/do
1/f = 1/-33.25 + 1/9.5
1/f = 0.075
I don't understand why this isn't right??

What are the units of f in 1/f when you want 1/f to be in diopters??

(If 1/f is in diopters, f is in meters).

The magnification is negative; di is positive. If you do that, it should work out.

Go with Gene N. but also pay attention to what kuruman said. Together they have the answer!

## What is the power of the lens in diopters?

The power of a lens is a measure of its ability to bend light. It is measured in diopters (D) and is represented by the symbol "D". The power of a lens is determined by its focal length, which is the distance from the lens to the point where light rays converge.

## How is the power of a lens calculated?

The power of a lens can be calculated using the formula P = 1/f, where P is the power in diopters and f is the focal length in meters. For example, a lens with a focal length of 0.5 meters would have a power of 1/0.5 = 2 D.

## What is the relationship between power and focal length?

The power of a lens is inversely proportional to its focal length. This means that as the focal length decreases, the power of the lens increases, and vice versa. For example, a lens with a shorter focal length will have a higher power and will be able to bend light rays more strongly than a lens with a longer focal length.

## How does the power of a lens affect its ability to refract light?

The power of a lens determines how much it can bend light rays. A lens with a higher power will be able to bend light more, resulting in a stronger refraction. This is why lenses with higher powers, such as those used for correcting nearsightedness, are thicker in the center and thinner at the edges.

## What are some common objects or materials with comparable power to a lens in diopters?

A lens with a power of 1 D is roughly equivalent to the refractive power of a glass window, while a lens with a power of 2 D is similar to the refractive power of a magnifying glass. A lens with a power of 4 D is comparable to the refractive power of a reading glasses, and a lens with a power of 10 D is similar to the refractive power of a microscope.

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