Question

Предмет высотой 6 мм находится на расстоянии 24 см от собирающей линзы с фокусным расстоянием 8см. Какова высота изображения предмета?

Answer 1

Найдём расстояние от линзы до изображения по формуле тонкой линзы:
1/d + 1/f = 1/F
1/f = 1/F - 1/d = 1/(8 см) - 1/(24 см) = 1/(12 см)
f = 12 см

Тогда увеличение Г = H/h = f/d = 12/24 = 0.5
Высота изображения H = Гh = 3 мм

Ответ. 3 мм 

Answer 2

Calculation of Image Height

To calculate 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, and - u is the object distance from the lens.

In this case, the object distance u is given as 24 cm, and the focal length f is given as 8 cm.

Let's substitute these values into the lens formula and solve for v:

1/8 = 1/v - 1/24.

To simplify the equation, we can find the common denominator:

1/8 = (24 - v)/(24v).

Now, cross-multiply and solve for v:

24v = 8(24 - v).

24v = 192 - 8v.

32v = 192.

v = 6.

Therefore, the image distance v is 6 cm.

To find the height of the image, we can use the magnification formula:

m = -v/u,

where m is the magnification, v is the image distance, and u is the object distance.

In this case, the object height is given as 6 mm (or 0.6 cm).

Let's substitute the values into the magnification formula and solve for the image height:

m = -6/24.

m = -1/4.

Therefore, the magnification is -1/4. Since the magnification is negative, the image is inverted.

To find the image height, we can use the formula:

h' = m * h,

where h' is the image height and h is the object height.

Let's substitute the values into the formula and solve for h':

h' = (-1/4) * 0.6.

h' = -0.15.

Therefore, the height of the image formed by the lens is -0.15 cm.

Please note that the negative sign indicates that the image is inverted.

Answer:

The height of the image formed by the lens is -0.15 cm.