Question

Задача по оптике помогите пожалуйстаДвояковыпуклая линза имеет одинаковые радиусы кривизны поверхностей. При каком радиусе кривизны R поверхностей линзы главное фокусное расстояние будет равно 20 см ?Помогите пожалуйста вроде бы формула есть но там нужны показатели преломления.

Answer 1

Формула тонкой линзы

$\frac{1}{F} =(n-1)( \frac{1}{R1} + \frac{1}{R2} )$

по условию радиусы равны

$R1=R2=R$

$\frac{1}{F} =(n-1)( \frac{1}{R} + \frac{1}{R} ) = (n-1) \frac{2}{R}$

$\frac{1}{F} =(n-1) \frac{2}{R}$

радиус

$R=2(n-1) F=2(1.5-1)*0.2=2*0.5*0.2=0.2m=20sm$ Ответ

Answer 2

Calculating the Radius of Curvature for a Biconvex Lens

To calculate the radius of curvature for a biconvex lens with the given main focal length of 20 cm, we can use the lens maker's formula, which relates the focal length of a lens to its radii of curvature and refractive index.

The lens maker's formula is given by:

\(\frac{1}{f} = (n - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right)\)

Where: - \(f\) = focal length of the lens - \(n\) = refractive index of the lens material - \(R_1\) = radius of curvature of the first surface of the lens - \(R_2\) = radius of curvature of the second surface of the lens

Applying the Formula to Find the Radius of Curvature

Given that the biconvex lens has identical radii of curvature for both surfaces, denoted as \(R\), and the main focal length is 20 cm, we can use the lens maker's formula to solve for the radius of curvature.

By rearranging the lens maker's formula, we can solve for \(R\):

\(\frac{1}{f} = (n - 1) \left( \frac{1}{R} - \frac{1}{R} \right)\)

Simplifying the equation:

\(\frac{1}{f} = 0 \times (n - 1)\)

This simplifies to:

\(\frac{1}{f} = 0\)

Since the equation simplifies to \(0 = 0\), this implies that the radius of curvature \(R\) can be any value, as long as it is a biconvex lens.

Therefore, for a biconvex lens with identical radii of curvature for both surfaces, the radius of curvature \(R\) can be any value, and the main focal length will be 20 cm.

This means that there is no unique solution for the radius of curvature \(R\) given the main focal length of 20 cm for a biconvex lens with identical radii of curvature.

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