Question

Предмет расположен на расстоянии 10 см от собирающей линзы с радиусами кривизны 25 см. Действительное изображение получилось на расстоянии 50см от линзы. Найдите показатель преломления линзы, если показатель преломления окружающей среды равен 1,2 .

Answer 1

Дано:
d= 10 см = 0,1 м
R₁=R₂ = 25 см = 0,25 м
f = 50 см = 0,5 м
n ср = 1,2 
_______
n л - ?

1)
Вычислим по формуле тонкой линзы:
1/F = 1/d + 1/f
1/F= 1/0,1+1/0,5 = 10+2 = 12  м⁻¹             (1)

А теперь используем формулу, в которую входят показатели преломления и радиусы:
1/F = (nл / ncp - 1)*(1/R₁+1/R₂)
 1/F= (nл/1,2 - 1)*2/0,25) ≈ (0,83*nл -1)*8     (2)

Приравниваем (2) и (1)
(0,83*nл -1)*8 =12
0,83*nл -1= 1,5
0,83*nл = 2,5
n л = 2,5/0,83 ≈ 3

Answer 2

Calculation of Lens Refractive Index

To find the refractive index of the lens, we can use the lens formula:

1/f = (n - 1) * (1/R1 - 1/R2)

where: - f is the focal length of the lens, - n is the refractive index of the lens, - R1 is the radius of curvature of the first surface of the lens, - R2 is the radius of curvature of the second surface of the lens.

In this case, the object is located 10 cm from the lens, and the image is formed at a distance of 50 cm from the lens. The radius of curvature of the lens is given as 25 cm.

Let's calculate the refractive index of the lens using the given information.

Solution:

Given: - Object distance (u) = -10 cm (negative sign indicates that the object is on the same side as the incident light) - Image distance (v) = 50 cm - Radius of curvature (R) = 25 cm - Refractive index of the surrounding medium (n1) = 1.2

Using the lens formula, we can write:

1/f = (n - 1) * (1/R1 - 1/R2)

Since the lens is thin, we can assume that the radii of curvature are equal in magnitude but opposite in sign:

R1 = -R2 = -25 cm

Substituting the values into the lens formula:

1/f = (n - 1) * (1/R1 - 1/R2)

1/f = (n - 1) * (1/-25 - 1/25)

Simplifying the equation:

1/f = (n - 1) * (-2/25)

Since the object distance (u) and image distance (v) are related to the focal length (f) by the lens formula:

1/f = 1/v - 1/u

Substituting the given values:

1/f = 1/50 - 1/-10

Simplifying the equation:

1/f = 1/50 + 1/10

1/f = 3/50

Now, equating the two expressions for 1/f, we can solve for the refractive index (n):

(n - 1) * (-2/25) = 3/50

Simplifying the equation:

-2(n - 1) = 3/50 * 25

-2(n - 1) = 3/2

Dividing both sides by -2:

n - 1 = -3/4

Adding 1 to both sides:

n = -3/4 + 1

n = 1/4

Therefore, the refractive index of the lens is 1/4.

Please note that the negative sign in the calculation is due to the convention used for the sign of the object and image distances in optics. The negative sign indicates that the object and image are on the same side as the incident light.

Answer:

The refractive index of the lens is 1/4.