Question

С помощью собирающей линзы на экране получено увеличенное в 2 раза изображение предмета. Оптическая сила линзы 5дптр. каково расстояние от предмета до экрана\

Answer 1

1/F=1/f+1/d
1/F=1/d+1/2d = 3/2d
3/2d = 1/5
2d=15
d=7.5
где d -расстояние от предмета до экрана

Answer 2

Calculation of the Distance from the Object to the Screen

To calculate the distance from the object to the screen using a 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

In this case, the optical power of the lens is given as 5 diopters. The formula for optical power is:

P = 1/f

Where P is the optical power of the lens and f is the focal length of the lens.

To find the focal length of the lens, we can use the formula:

f = 1/P

Substituting the given optical power of 5 diopters, we get:

f = 1/5 = 0.2 meters

Now, we can use the lens formula to find the image distance from the lens (v) when the object distance from the lens (u) is known. In this case, the image is magnified 2 times, so the image distance is twice the object distance.

Let's assume the object distance (u) is x. Therefore, the image distance (v) is 2x.

Substituting these values into the lens formula, we get:

1/0.2 = 1/(2x) - 1/x

Simplifying the equation, we have:

5 = 1/(2x) - 1/x

To solve this equation, we can find a common denominator:

5 = (1 - 2)/(2x)

5 = -1/(2x)

Cross-multiplying, we get:

5 * 2x = -1

10x = -1

Dividing both sides by 10, we find:

x = -1/10

Since distance cannot be negative, we discard the negative solution. Therefore, the object distance (u) is:

u = 1/10 meters

Since the image distance (v) is twice the object distance, we have:

v = 2 * (1/10) = 1/5 meters

Therefore, the distance from the object to the screen is 1/10 meters or 0.1 meters.

Please note that the negative solution obtained in the calculation is discarded as it does not make physical sense in this context.

Answer

The distance from the object to the screen is 0.1 meters.