Question

На екрані, розташованому на відстані 60 см від тонкої лінзи з оптичною силою 5 дптр, отримали чітке зображення предмета. Предмет відсувають на 10 см далі від лінзи. На скільки сантиметрів слід перемістити екран, щоб одержати на ньому чітке зображення? Допоможіть будь ласка!!!!!!

Answer 1

Ответ:

Розв'язок на фото)

Объяснение:

Answer 2

Optics Problem: Image Distance Adjustment

To solve this problem, we can use the lens formula:

1/f = 1/v - 1/u

Where: - f = focal length of the lens - v = image distance - u = object distance

Given: - Object distance, u = 60 cm - Focal length, f = 1/5 meters (since the unit of optical power diopters (D) is defined as the reciprocal of the focal length in meters)

We can first calculate the image distance v using the lens formula.

Calculating Image Distance:

Using the lens formula, we can calculate the initial image distance:

1/f = 1/v - 1/u

Plugging in the values: 1/5 = 1/v - 1/60

Solving for v: 1/v = 1/5 + 1/60 1/v = (12 + 1)/60 1/v = 13/60 v = 60/13 v ≈ 4.62 cm

So, the initial image distance v is approximately 4.62 cm.

Adjusting Image Distance:

Now, the object is moved 10 cm further away from the lens, so the new object distance u' = 60 cm + 10 cm = 70 cm.

We need to find the new image distance v' to obtain a clear image on the screen.

Calculating New Image Distance:

Using the lens formula again with the new object distance u':

1/f = 1/v' - 1/u'

Plugging in the values: 1/5 = 1/v' - 1/70

Solving for v': 1/v' = 1/5 + 1/70 1/v' = (14 + 1)/70 1/v' = 15/70 v' = 70/15 v' = 4.67 cm

So, the new image distance v' is approximately 4.67 cm.

Conclusion:

To obtain a clear image on the screen after moving the object 10 cm further away from the lens, the screen should be moved approximately 0.05 cm further from the lens.

I hope this helps! If you have any more questions or need further assistance, feel free to ask!