Question

Тонкая стеклянная линза ( n = 1,5 ) имеет оптическую силу 5 дптр. Та же линза, погружённая в жидкость, действует как линза с оптической силой (-I) дптр. Определить показатель преломления жидкости.

Answer 1

Тонкая стеклянная линза ( n = 1,5 ) имеет оптическую силу 5 дптр. Та же линза, погружённая в жидкость, действует как линза с оптической силой (-I) дптр. Определить показатель преломления жидкости.

n=1,5    n1=1   D1=5 дптр   D2=-1 дптр    n2-?

по формуле тонкой линзы
D1=(n-1)*(1/R1+!/R2)
D2=(n-n2)*(1/R1+1/R2)
D2/D1=(n-n2)/(n-1)
-1/5=(1,5-n2)/0,5
-0,5=7,5-5*n2
n2=8/5=1,6

Ответ n2=1,6

Answer 2

Calculation of the Refractive Index of the Liquid

To determine the refractive index of the liquid, we can use the formula for the power of a lens:

Power of a lens (P) = 1 / focal length (f)

The power of the lens in air is given as 5 diopters (D), and the power of the lens in the liquid is given as -I diopters (D).

Since the power of a lens is inversely proportional to its focal length, we can write:

P_air = 1 / f_air

P_liquid = 1 / f_liquid

Given that the refractive index of air (n_air) is approximately 1, we can rewrite the equations as:

P_air = n_air / f_air

P_liquid = n_liquid / f_liquid

Since the lens is the same in both cases, the focal length remains constant. Therefore, we can equate the two equations:

P_air = P_liquid

n_air / f_air = n_liquid / f_liquid

Simplifying the equation, we get:

n_liquid = n_air * (f_liquid / f_air)

Given that the refractive index of air (n_air) is 1.5 and the power of the lens in air (P_air) is 5 diopters, we can substitute these values into the equation:

n_liquid = 1.5 * (f_liquid / f_air)

However, we still need to determine the ratio of the focal lengths (f_liquid / f_air). To do this, we can use the lens formula:

1 / f = (n_liquid - n_air) * (1 / R1 - 1 / R2)

Where: - f is the focal length of the lens - n_liquid is the refractive index of the liquid - n_air is the refractive index of air - R1 and R2 are the radii of curvature of the lens surfaces

Unfortunately, the radii of curvature of the lens surfaces are not provided in the question. Therefore, we cannot calculate the exact refractive index of the liquid without this information.

Please provide the radii of curvature of the lens surfaces so that we can proceed with the calculation.