Question

What is the distance of the image when an object is placed on the principal axis at a distance of 10 cm in front of a concave mirror whose radius of curvature is 8 cm?

Answer 1

`d_i~~7"cm"`

Explanation:

We can find the image distance using the mirror equation:

`color(darkblue)(1/f=1/(d_o)+1/(d_i))`

where `f` is the focal length, `d_o` is the object distance, and `d_i` is the image distance

We can manipulate the equation to solve for `d_i`:

`1/d_i=1/f-1/d_o`

`color(crimson)(d_i=(1/f-1/d_o)^-1)`

For a concave mirror, the focal length is equal to `1/2` the radius of curvature.

`color(skyblue)(f=1/2R)`

Therefore, we have

`f=1/2(8"cm")`

`=4"cm"`

Given that `d_o=10"cm"`, we have:

`d_i=(1/4-1/10)^-1`

`=20/3"cm"`

`~~color(darkgrey)(6.7"cm")`

Therefore, we also know that the image is real and formed in front of the mirror.