Question

Suppose that you place an object along the principal axis of a concave spherical mirror, exactly halfway to the center of the curvature (half of the radius). What will the result be?

Answer 1

Answer:

There will be no clear image of the object.

Explanation:

For a concave spherical mirror, we have the distance from center of curvature to the mirror is the radius of curvature, R, and half of the length of the radius of curvature is the focal length, f, of the mirror, that is we have;

$f = \dfrac{R}{2}$

From the equation of a mirror in optics we have;

$\dfrac{1}{f} = \dfrac{1}{d_o} + \dfrac{1}{d_i}$

Where:

$d_o$ = Distance of the object from the mirror

$d_i$ = Distance of the image from the mirror

Hence, where the object distance is half the radius of curvature or f, we have;

$\dfrac{1}{f} = \dfrac{1}{f} + \dfrac{1}{d_i}$

Therefore, the location of the image formed will be at;

$\dfrac{1}{d_i}= \dfrac{1}{f} - \dfrac{1}{f} = 0$

$d_i = \dfrac{1}{0}= \infty$

Hence, since the location of the image formed will be at infinity there will be no clear image of the object.

Answer 2

Answer:

A clear image of that object won't be formed at all.

Explanation:

PF The point exactly halfway to the center of curvature of a concave spherical mirror is called the center of curvature. The point exactly halfway from the mirror to the center is called the focal point (or focus) of the mirror. When the object is exactly at the focus of the mirror, the reflecting rays are parallel and therefore won't meet to form an image.