Question

Коллекционер разглядывает при помощи лупы элемент марки, имеющий размер 0,2 мм, и видит его мнимое изображение, увеличенное до 1,2 мм. Рассматриваемый элемент расположен на расстоянии 7 мм от лупы. На каком расстоянии от лупы находится его изображение? Ответ выразить в мм.

Answer 1

f/d=1,2/0,2=6
d=7 мм
f=7*6 мм = 42 мм

Answer 2

Calculation of the Image Distance

To determine the distance at which the image of the element is located from the magnifying glass, we can use the magnification formula:

Magnification (m) = Image Height (h_i) / Object Height (h_o)

In this case, the magnification is given as 1.2, and the object height is 0.2 mm. Therefore, we can rewrite the formula as:

1.2 = h_i / 0.2

To find the image height (h_i), we can rearrange the equation:

h_i = 1.2 * 0.2

Calculating this, we find that the image height is 0.24 mm.

Calculation of the Image Distance

To find the distance at which the image is located from the magnifying glass, 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, - u is the object distance.

In this case, the object distance (u) is given as 7 mm. We need to find the image distance (v).

Focal Length of the Magnifying Glass

To calculate the focal length of the magnifying glass, we can use the lens formula again:

1/f = 1/v - 1/u

Rearranging the equation, we get:

1/v = 1/f + 1/u

Since the magnifying glass is being used as a simple magnifier, we can assume that the object is placed at the focal length of the lens. Therefore, the object distance (u) is equal to the focal length (f).

Substituting the values into the equation, we have:

1/v = 1/f + 1/f

Simplifying this, we get:

1/v = 2/f

Rearranging the equation, we find:

v = f/2

Calculation of the Image Distance

Now that we know the object distance (u) is equal to the focal length (f), we can substitute the values into the lens formula:

1/f = 1/v - 1/u

Substituting v = f/2 and u = f, we have:

1/f = 1/(f/2) - 1/f

Simplifying this equation, we get:

1/f = 2/f - 1/f

Combining the fractions, we have:

1/f = 1/f

This equation shows that the focal length (f) is equal to itself, which is true for any lens.

Therefore, the image distance (v) is equal to half the focal length (f).

Conclusion

In this case, the object distance (u) is given as 7 mm. Since the object distance is equal to the focal length (u = f), the image distance (v) is equal to half the focal length:

v = f/2 = 7 mm / 2 = 3.5 mm

Therefore, the image of the element is located at a distance of 3.5 mm from the magnifying glass.

Please note that the calculations assume ideal conditions and do not take into account any aberrations or other factors that may affect the image formation.