Question

Оптическая сила линзы равна 10 дптр. Перед ней на расстоянии равном 15 см находится линейный предмет высотой 2 см перпендикулярно главной оптической оси линзы. Найдите высоту изображения.

Answer 1

D=10 дптр   d=15 см   h=2 см   H=?

D=1/F=1/d+1/f

H/h=f/d

F=1/D=1/10=0.1 м (10 см)

f=F*d/(d-F)=10*15/(15-10)=30 см расстояние от линзы до изображения

H=f*h/d=30*2/15=4 см

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Answer 2

Calculation of Image Height

To find the height of the image formed by the lens, 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 from the lens - u is the object distance from the lens

In this case, the optical power of the lens is given as 10 D (diopters). The focal length (f) of a lens in meters can be calculated using the formula:

f = 1 / P

Where P is the optical power of the lens in diopters.

Let's calculate the focal length of the lens first:

f = 1 / P = 1 / 10 = 0.1 meters

The object distance (u) is given as 15 cm, which is equal to 0.15 meters.

Now, we can substitute the values of f and u into the lens formula to find the image distance (v):

1/0.1 = 1/v - 1/0.15

Simplifying the equation:

10 = 1/v - 6.67

1/v = 10 + 6.67

1/v = 16.67

v = 1 / 16.67

v ≈ 0.06 meters

The height of the object (h) is given as 2 cm, which is equal to 0.02 meters.

To find the height of the image (h'), we can use the magnification formula:

h' / h = -v / u

Substituting the values:

h' / 0.02 = -0.06 / 0.15

Simplifying the equation:

h' / 0.02 = -0.4

h' = -0.4 * 0.02

h' = -0.008 meters

Since the height of the image cannot be negative, we take the absolute value:

h' ≈ 0.008 meters

Therefore, the height of the image formed by the lens is approximately 0.008 meters.