Answer:
n = 1 + R / f
Explanation:
The equation of the constructor is optical is
1 / f = 1 / p + 1 / q
where f is the focal length, p and q are the distance to the object and image, respectively
The exercise tells us that it is a concave lens with focal length fo, in these lenses the focal length is negative. The relationship to calculate the focal length is
1 / f = (n -n₀) (1 /R₁ - 1 /R₂)
where is n₀ the refractive index of the medium that surrounds the lens in this case it is air with n₀ = 1, you do not indicate the type of lens, but the most used lens is the concave plane, in this case R₂ = ∞, so which 1 / R₂ = 0, let's substitute
1 / f = (n-1) / R₁
n - 1 = R₁ / f
let's calculate
n = 1- R₁ / f
remember that the radius of curvature is negative, so the equation is
n = 1 + R / f
