Question

На расстоянии d =15 см собирающей линзы с оптической силой D= 10 дптр находится предмет высотой h=5 см. найдите h' и расстояние f от линзы до изображения

Answer 1

на расстоянии d =15 см собирающей линзы с оптической силой D= 10 дптр находится предмет высотой h=5 см. найдите H - ? и расстояние f  - ? от линзы до изображения

по формуле линзы  D= 1/d +1/f
1/f=D-1/d=10-1/0,15=3,333
f=1/3,3333=0,3 м=30 cм
Г=f/d=30/15=2
H=h*2=5*2=10 см

Ответ f=30 см  H=10 см

Answer 2

Given Parameters

The given parameters for the problem are: - Object distance, d = 15 cm - Optical power of the lens, D = 10 diopters - Object height, h = 5 cm

Calculating Image Height (h')

To find the image height, we can use the lens equation:

1/f = 1/d_o + 1/d_i

Where: - f is the focal length of the lens - d_o is the object distance - d_i is the image distance

First, let's calculate the focal length of the lens using the given optical power:

f = 1 / D

Substitute the value of D to find f: f = 1 / 10 = 0.1 m = 10 cm.

Now, we can use the lens equation to find the image distance d_i: 1/10 = 1/15 + 1/d_i

Solving for d_i: 1/d_i = 1/10 - 1/15 = (3 - 2) / 30 = 1/30 d_i = 30 cm.

Now, we can use the magnification formula to find the image height h': h' = h * (d_i / d_o)

Substitute the given values: h' = 5 * (30 / 15) = 10 cm.

So, the image height h' is 10 cm.

Calculating Image Distance (f')

To find the image distance, we can use the lens formula: 1/f' = 1/d_o + 1/d_i

Substitute the given values: 1/f' = 1/15 + 1/30 = (2 + 1) / 30 = 1/10 f' = 10 cm.

So, the image distance f' from the lens to the image is 10 cm.

Therefore, the image height h' is 10 cm and the image distance f' from the lens to the image is 10 cm.