Question

на экране с помощью собирающей линзы было получено увеличенное в раза изображение предмета оптическая сила линзы от 5 до 10 дптр каково может быть расстояние от предмета до экрана?

Answer 1

Запишем формулу оптической силы линзы , F - фокусное растояние (м). Если оптическая сила равна 5 дптр, то , F = 0,2 м.

Если же оптическая сила равна 10 дптр то, , F = 0,1. 

Расстояние от предмета до экрана есть , два фокусных расстояния, так как изображение полученное с помощью линзы, увеличиное в 2 раза, а сама линза собирающая.

ответ: 15

Answer 2

Optics and Lens Magnification

When using a converging lens to obtain an enlarged image of an object on a screen, the optical power of the lens can be used to calculate the distance from the object to the screen. In this case, the optical power of the lens changes from 5 to 10 diopters.

The formula to calculate the distance from the object to the screen when the optical power of the lens changes is given by:

\[ \frac{1}{f} = (n-1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right) \]

Where: - \( f \) = focal length of the lens - \( n \) = refractive index of the medium - \( R_1 \) and \( R_2 \) = radii of curvature of the lens surfaces

Given that the optical power \( D \) of a lens is related to the focal length \( f \) by the equation \( D = \frac{1}{f} \), we can use the relationship between optical power and focal length to calculate the distance from the object to the screen.

Calculation

When the optical power of the lens changes from 5 to 10 diopters, the focal length \( f \) of the lens changes accordingly. Using the relationship \( D = \frac{1}{f} \), we can calculate the new focal length and then use it to find the distance from the object to the screen.

Given: - Initial optical power \( D_1 = 5 \, D \) - Final optical power \( D_2 = 10 \, D \)

Using the relationship \( D = \frac{1}{f} \), we can calculate the initial and final focal lengths:

For the initial optical power: \[ D_1 = \frac{1}{f_1} \] \[ f_1 = \frac{1}{D_1} = \frac{1}{5} \]

For the final optical power: \[ D_2 = \frac{1}{f_2} \] \[ f_2 = \frac{1}{D_2} = \frac{1}{10} \]

Now, we can use the formula for the relationship between the focal length and the distance from the object to the screen:

\[ \frac{1}{f_2} = (n-1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right) \]

By substituting the values of \( f_2 \), \( n \), \( R_1 \), and \( R_2 \) into the equation, we can solve for the distance from the object to the screen.

Conclusion

The distance from the object to the screen can be calculated using the change in optical power of the lens and the relationship between optical power, focal length, and the distance from the object to the screen.