Question

Линза с фокусным расстоянием 20 см дает уменьшенное в 4 раза изображение предмета.Сему равно расстояние от предмета до линзы и от линзы до иизображения

Answer 1

По условию d/f= 4
d=4*f
по формуле линзы 1/F= 1/d +1/f
1/F=1/4*f   +1/f = 5/4*f
f=5*20/4=25 см
d=25*4=100 см

Answer 2

Calculation of Distance from Object to Lens and Lens to Image

To calculate the distances from the object to the lens and from the lens to the image, we can use the lens formula:

1/f = 1/v - 1/u

Where: - f is the focal length of the lens - v is the distance from the lens to the image (image distance) - u is the distance from the object to the lens (object distance)

In this case, we are given that the lens has a focal length of 20 cm and it produces a magnification of 4x (the image is 4 times smaller than the object). We need to find the values of v and u.

Let's solve the equation step by step:

1. We know that the magnification (m) is given by the formula:

m = -v/u

Since the image is 4 times smaller, the magnification is -4. Therefore:

-4 = -v/u

2. We can rearrange the equation to solve for v:

v = 4u

3. Now, let's substitute this value of v into the lens formula:

1/20 = 1/(4u) - 1/u

4. Simplifying the equation:

1/20 = (1 - 4)/(4u)

1/20 = -3/(4u)

5. Cross-multiplying:

4u = -60

6. Solving for u:

u = -60/4

u = -15 cm

7. Now, substitute the value of u back into the equation to find v:

v = 4u

v = 4(-15)

v = -60 cm

Answer:

The distance from the object to the lens is -15 cm and the distance from the lens to the image is -60 cm.

Please note that the negative sign indicates that the distances are measured on the opposite side of the lens from the object and image, respectively.