Question

Предмет высотой 6 см расположен на главной оптической оси тонкой собирающей линзы на расстоянии 30 см от ее оптического центра .Оптическая сила линзы 5дптр. найдите высоту изображения

Answer 1

Дано
h=6см=0,06м
d=30см=0,3м
D=5Дптр
Н-?
Формула тонкой линзы
D=1/d+1/f
1/f=D-1/d
f=1/( D-1/d)
f=0,6м расстояние до изображения
Линейное увеличение
Г= H/h= f/d
H/0,06=0,6/03
Н/0,06=2
Н=2×0,06=0,12=12 см

Ответ 12см

Answer 2

Calculation of Image Height

To find the height of the image formed by the thin converging lens, 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 from the lens - u is the object distance from the lens

In this case, the object is located on the principal optical axis of the lens, so the object distance (u) is positive.

Given: - Object height (h) = 6 cm - Object distance (u) = 30 cm - Optical power of the lens (P) = 5 D

To find the image height (h'), we need to find the image distance (v) first.

Finding the Image Distance

The optical power of a lens is given by the formula:

P = 1/f

Where P is the optical power of the lens and f is the focal length of the lens.

In this case, the optical power (P) is given as 5 D. We can use this information to find the focal length (f) of the lens.

From the lens formula, we can rearrange it to solve for the image distance (v):

1/v = 1/f - 1/u

Substituting the given values: - P = 5 D - u = 30 cm

We can calculate the focal length (f) using the formula:

f = 1/P

Then, substitute the values of f and u into the lens formula to find v.

Calculation Steps

1. Calculate the focal length (f) using the formula f = 1/P. 2. Substitute the values of f and u into the lens formula to find v. 3. Once we have the value of v, we can calculate the image height (h') using the magnification formula:

h'/h = -v/u

Substitute the values of h and v into the magnification formula to find h'.

Calculation

1. Calculate the focal length (f): - P = 5 D - f = 1/P = 1/5 = 0.2 m = 20 cm

2. Substitute the values of f and u into the lens formula to find v: - 1/v = 1/f - 1/u - 1/v = 1/20 - 1/30 - 1/v = (3 - 2)/60 - 1/v = 1/60 - v = 60 cm

3. Calculate the image height (h'): - h'/h = -v/u - h' = -v/u * h - h' = -60/30 * 6 - h' = -2 * 6 - h' = -12 cm

Answer

The height of the image formed by the thin converging lens is 12 cm.