# Optics - spherical and plane mirror

#### asteeves_

1. Homework Statement

A convex spherical mirror with a focal length of magnitude 24.0 cm is placed 22.0 cm to the left of a plane mirror. An object 0.300 cm tall is placed midway between the surface of the plane mirror and the vertex of the spherical mirror. The spherical mirror forms multiple images of the object.

-Where are the two images of the object formed by the spherical mirror that are closest to the spherical mirror?

-How tall is each image?

2. Homework Equations

(1) 1/f=1/s+1/s'
(2) y'/y = -s'/s

3. The Attempt at a Solution

Using initial conditions and equation 1 I solved for the first s' (=-7.54), my next thought was to use this number in place of s and solve again for s' since the reflection off the plane mirrior will land right back where it was originally, however I am not getting the correct answer and am unsure what else to do.

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#### haruspex

Homework Helper
Gold Member
2018 Award
use this number in place of s and solve again for s' since the reflection off the plane mirrior will land right back where it was originally,
Not sure exactly what you are saying. s and s' are measured from the convex mirror, right? The image in the plane mirror should involve the distance to the plane mirror.
Also need to consider order of reflections, plane mirror first or convex first.

#### asteeves_

Not sure exactly what you are saying. s and s' are measured from the convex mirror, right? The image in the plane mirror should involve the distance to the plane mirror.
Also need to consider order of reflections, plane mirror first or convex first.
How exactly do you determine the order of reflection?

#### haruspex

Homework Helper
Gold Member
2018 Award
How exactly do you determine the order of reflection?
Both orders will occur, and multiple images for each order as the light bounces back and forth between the mirrors.
Of all these, you are asked for the two images which a) involve at least one reflection in the spherical mirror and b) are nearest that mirror.

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