Question

Предмет высотой 5 см находятся на расстоянии 30 см от собирающей тонкой линзы определить высоту изображения если извесно что оптическая сила линзы состовляет 5 диоптрии

Answer 1

Ответ:

Объяснение:

Дано:

h = 30 см

d = 30 см

D = + 5 дптр

____________

H - ?

1)

Определим фокусное расстояние линзы:

F = 1 / D = 1 / 5 = 0,2 м  или  F = 20 см

2)

Определим расстояние до изображения из формулы тонкой линзы:

1 / F = 1 / d + 1 / f

1 / f = 1 / F - 1 / d

f = d·F / (d - F) = 30·20 / (30 - 20) = 60 см

3)

Высоту изображения найдем из формулы увеличения линзы:

Г = f / d = 60 / 30 = 2

Г = H / h

H = Г·h = 2·5 = 10 см

Answer 2

Calculating the Height of the Image Formed by a Thin Lens

To calculate the height of the image formed by a thin lens, we can use the lens formula:

1/f = 1/v - 1/u

Where: - f = focal length of the lens - v = image distance - u = object distance

Given: - Object height (h) = 5 cm - Object distance (u) = 30 cm - Optical power of the lens (P) = 5 diopters

Calculating the Focal Length of the Lens

First, let's calculate the focal length of the lens using the given optical power (P).

The formula to calculate the focal length from the optical power is:

f = 1/P

Substitute the given optical power into the formula:

f = 1/5 = 0.2 meters = 20 cm

Calculating the Image Distance

Now, we can calculate the image distance (v) using the lens formula.

1/f = 1/v - 1/u

Substitute the values: - f = 20 cm - u = 30 cm

1/20 = 1/v - 1/30

Solving for v: 1/v = 1/20 + 1/30 1/v = (3 + 2) / 60 1/v = 5 / 60 v = 60 / 5 = 12 cm

Calculating the Height of the Image

Finally, we can calculate the height of the image formed by the lens using the magnification formula:

m = -v/u

Where: - m = magnification - v = image distance - u = object distance

Substitute the values: - v = 12 cm - u = 30 cm

m = -12/30 = -0.4

The negative sign indicates that the image is inverted.

Now, we can calculate the height of the image: h' = m * h h' = -0.4 * 5 = -2 cm

Conclusion

The height of the image formed by the thin lens is 2 cm and it is inverted.