Question

Предмет высотой 6 см расположен на главной оптической оси тонкой собирательной линзы расположенной на расстоянии 30см от ее оптического центра. Оптическая сила линзы 5 д. Найдите высоту изображения предмета

Answer 1

Решение во вложении:

Answer 2

Calculation of Image Height

To find the height of the image formed by the thin converging 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.

Given: - The object height is 6 cm. - The lens is a thin converging lens with an optical power of 5 D (diopters). - The lens is located at a distance of 30 cm from its optical center.

We need to find the height of the image formed by the lens.

Solution:

First, let's find the focal length of the lens using the formula:

f = 1 / P,

where P is the optical power of the lens.

Given that the optical power of the lens is 5 D, we can calculate the focal length:

f = 1 / 5 = 0.2 m.

Next, let's find the image distance v using the lens formula:

1/f = 1/v - 1/u.

Since the lens is located at a distance of 30 cm from its optical center, the object distance u is equal to -30 cm (negative because the object is on the same side as the lens).

Substituting the values into the lens formula:

1/0.2 = 1/v - 1/-30.

Simplifying the equation:

5 = 1/v + 1/30.

To solve for v, we can rearrange the equation:

1/v = 5 - 1/30.

1/v = (150 - 1) / 30.

1/v = 149 / 30.

v = 30 / 149.

Using a calculator, we find that v ≈ 0.2013 m.

Now, let's find the magnification m of the lens using the formula:

m = -v / u.

Substituting the values:

m = -0.2013 / -0.3.

Simplifying the equation:

m = 0.2013 / 0.3.

Using a calculator, we find that m ≈ 0.671.

Finally, we can find the height of the image h' using the formula:

h' = m * h,

where h is the height of the object.

Substituting the values:

h' = 0.671 * 6.

Using a calculator, we find that h' ≈ 4.026 cm.

Therefore, the height of the image formed by the thin converging lens is approximately 4.026 cm.

Answer:

The height of the image formed by the thin converging lens is approximately 4.026 cm.