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

There will be no clear image of the object.

Step-by-step 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 = (R)/(2)`

From the equation of a mirror in optics we have;

`(1)/(f) = (1)/(d_o) + (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;

`(1)/(f) = (1)/(f) + (1)/(d_i)`

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

`(1)/(d_i)= (1)/(f) - (1)/(f) = 0`

`d_i = (1)/(0)= \infty`

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