Question

Линза с фокусным расстоянием F=1м дает на экране изображение предмета, уменьшенное в 4 раза. Каково расстояние от предмета до линзы?

Answer 1

Увеличение Г= f/d, откуда f = Гd

Формула линзы 1/F = 1/d +1/f = 1/d +1/Гd = (1+ 1/Г)/d

Перевернём дроби F = d/(1+ 1/Г)

Отсюда d = F(1+ 1/Г) = 1(1+4) = 5(м)

Answer 2

Calculation of the Distance from the Object to the Lens

To calculate the distance from the object to 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 (distance from the lens to the image) - u is the object distance (distance from the lens to the object)

Given that the focal length of the lens is F = 1m and the image is reduced by a factor of 4, we can determine the image distance:

v = -4u

Substituting this value into the lens formula, we have:

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

Simplifying the equation, we get:

1 = -1/4u - 1/u

Combining the fractions, we have:

1 = (-1 - 4)/4u

Simplifying further, we get:

1 = -5/4u

To solve for u, we can cross-multiply:

u = -4/5

Therefore, the distance from the object to the lens is -0.8m.

Please note that the negative sign indicates that the object is located on the same side of the lens as the incident light.