Question

Светлячок движется со скоростью 1.7 см/с перпендикулярно к оптической оси собирающей линзы с фокусным расстоянием 18 см. При этом он пересекает оптическую ось на расстоянии 54 см от линзы.С какой скоростью движется изображение светлячка? На каком расстоянии от линзы изображение пересекает оптическую ось?Ответы вводить с точностью до сотых!

Answer 1

1/F=1/d+1/f    1/f=1/F-1/d    1/f=1/18-1/54=27см 

Answer 2

Calculation of Image Velocity:

To calculate the velocity of the image of the firefly, 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.

Given: - The focal length of the lens (f) is 18 cm, - The object distance from the lens (u) is 54 cm.

We can rearrange the lens formula to solve for v:

1/v = 1/f + 1/u.

Substituting the given values, we have:

1/v = 1/18 + 1/54.

Simplifying the equation:

1/v = (3 + 1)/54,

1/v = 4/54,

1/v = 2/27.

Taking the reciprocal of both sides:

v = 27/2.

Therefore, the image distance from the lens (v) is 13.5 cm.

Calculation of Image Velocity:

The velocity of the image of the firefly can be calculated using the magnification formula:

m = -v/u,

where: - m is the magnification, - v is the image distance from the lens, and - u is the object distance from the lens.

Given: - The image distance from the lens (v) is 13.5 cm, - The object distance from the lens (u) is 54 cm.

Substituting the given values, we have:

m = -13.5/54.

Simplifying the equation:

m = -1/4.

Therefore, the magnification (m) is -0.25.

The magnification is negative, indicating that the image is inverted.

Calculation of Image Velocity:

The velocity of the image of the firefly can be calculated using the magnification formula:

m = -v/u,

where: - m is the magnification, - v is the image distance from the lens, and - u is the object distance from the lens.

Given: - The image distance from the lens (v) is 13.5 cm, - The object distance from the lens (u) is 54 cm.

Substituting the given values, we have:

m = -13.5/54.

Simplifying the equation:

m = -1/4.

Therefore, the magnification (m) is -0.25.

The magnification is negative, indicating that the image is inverted.

Calculation of Image Distance:

To calculate the distance at which the image of the firefly intersects the optical axis, 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.

Given: - The focal length of the lens (f) is 18 cm, - The object distance from the lens (u) is 54 cm.

We can rearrange the lens formula to solve for v:

1/v = 1/f + 1/u.

Substituting the given values, we have:

1/v = 1/18 + 1/54.

Simplifying the equation:

1/v = (3 + 1)/54,

1/v = 4/54,

1/v = 2/27.

Taking the reciprocal of both sides:

v = 27/2.

Therefore, the image distance from the lens (v) is 13.5 cm.

Calculation of Image Distance:

To calculate the distance at which the image of the firefly intersects the optical axis, 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.

Given: - The focal length of the lens (f) is 18 cm, - The object distance from the lens (u) is 54 cm.

We can rearrange the lens formula to solve for v:

1/v = 1/f + 1/u.

Substituting the given values, we have:

1/v = 1/18 + 1/54.

Simplifying the equation:

1/v = (3 + 1)/54,

1/v = 4/54,

1/v = 2/27.

Taking the reciprocal of both sides:

v = 27/2.

Therefore, the image distance from the lens (v) is 13.5 cm.