Question

a concave refracting surface of a medium with index of refraction n produces a real image no matter where an object is placed outside

only if the index of refraction of the surrounding medium is greater than n.
never.
always.
none of the choices are correct.
only if the index of refraction of the surrounding medium is less than n.

Explanation:

For a concave refracting surface, using the refraction formula \(\frac{n_2}{v}-\frac{n_1}{u}=\frac{n_2 - n_1}{R}\). When \(n_1>n_2\) (where \(n_1\) is the refractive index of the surrounding medium and \(n_2=n\) is the refractive index of the medium with the concave surface), for a real object (\(u<0\)), the image distance \(v\) will be negative (virtual image). When \(n_1 < n_2\), \(\frac{n_2}{v}=\frac{n_2 - n_1}{R}+\frac{n_1}{u}\). For a concave surface \(R<0\). If \(n_1 < n_2\), even for a real object (\(u<0\)), we cannot always get a real image. In fact, a concave refracting surface can never form a real image of an object placed outside.

Answer:

never.