Question

Палочка длиной 2 см расположена перед линзой с фокусным расстоянием 2 см так, что ближайший к линзе конец палочки находится на главной оптической оси линзы на расстоянии 3 см от линзы, а палочка образует угол 60 градусов с этой осью. Найти длину изображения палочки.

Answer 1

2,8 если линза собирающая 

Answer 2

Calculation of the Length of the Image of the Stick

To find the length of the image of the stick, 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 focal length of the lens is 2 cm, and the object distance from the lens is 3 cm. We need to find the image distance.

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

1/2 = 1/v - 1/3

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

3v - 2v = 2(3)

v = 6 cm

Now that we have the image distance, we can calculate the length of the image of the stick using the magnification formula:

magnification = -v/u

Where: - magnification is the ratio of the height of the image to the height of the object - v is the image distance from the lens - u is the object distance from the lens

In this case, the object distance is 3 cm and the image distance is 6 cm. Let's substitute these values into the magnification formula:

magnification = -6/3 = -2

The negative sign indicates that the image is inverted.

The length of the image of the stick can be calculated by multiplying the magnification by the length of the stick. Since the length of the stick is given as 2 cm, we can calculate the length of the image as:

length of the image = magnification * length of the stick = -2 * 2 = -4 cm

Therefore, the length of the image of the stick is 4 cm.