Question

Расстояние между предметом и его равным действительным изображением равно 1м. Определить фокусное расстояние линзы. Построить изображение.

Answer 1

Если H/h= 1  и по условию изображение действительное, то предмет поместили на расстоянии d= 2*F     и   f=2*F - расстояние от линзы до изображения
L = d+f=4*F
F =L/4=100/4=25 см
Ответ :    F=25 cм

Answer 2

Calculation of the focal length of the lens

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

1/f = 1/v - 1/u

where: - f is the focal length of the lens, - v is the distance between the lens and the real image, - u is the distance between the lens and the object.

In this case, the distance between the object and its real image is given as 1 meter. Let's assume that the distance between the lens and the object (u) is x meters. Therefore, the distance between the lens and the real image (v) would be (1 - x) meters.

Substituting these values into the formula, we get:

1/f = 1/(1 - x) - 1/x

Simplifying the equation, we can find the value of f.

Calculation of the focal length (f)

To calculate the focal length, we need to solve the equation:

1/f = 1/(1 - x) - 1/x

Let's solve this equation step by step:

1. Multiply both sides of the equation by f(x)(1 - x) to eliminate the denominators:

f(x) = (f(x)(1 - x))/(1 - x) - (f(x)(1 - x))/x

2. Simplify the equation:

f(x) = f(x) - xf(x) - (1 - x)f(x)

3. Combine like terms:

f(x) = f(x) - xf(x) - f(x) + xf(x)

4. Cancel out like terms:

0 = 0

Since the equation simplifies to 0 = 0, it means that the focal length (f) can be any value. Therefore, we cannot determine the exact focal length of the lens based on the given information.

Construction of the image

To construct the image, we need to know the type of lens being used (convex or concave) and the position of the object relative to the lens. Without this information, it is not possible to provide a specific construction for the image.

If you can provide more details about the lens and the object's position, I would be happy to assist you further in constructing the image.