What is the power of the lens in diopters?

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.
  • #1
KVM
1
0

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??
 
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  • #2
What are the units of f in 1/f when you want 1/f to be in diopters??
 
  • #3
(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.
 
  • #4
Go with Gene N. but also pay attention to what kuruman said. Together they have the answer!
 

Related to What is the power of the lens in diopters?

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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