An object that is 32 cm in front of a convex mirror has an image located 17 cm behind the mirror. How far behind the mirror is the image located when the object is 24 cm in front of the mirror?

Same thing here :(

To find the location of the image when the object is 24 cm in front of the mirror, we can use the mirror equation:

1/f = 1/d₀ + 1/dᵢ

where:
f is the focal length of the mirror,
d₀ is the distance of the object from the mirror, and
dᵢ is the distance of the image from the mirror.

In this case, we are given that the object is 32 cm in front of the mirror and that the image is located 17 cm behind the mirror. Let's plug in these values into the equation:

1/f = 1/32 cm + 1/(-17 cm)

Now, we can solve for f:

1/f = 1/32 cm - 1/17 cm
1/f = (17 - 32)/(17 * 32) cm
1/f = -15/(17 * 32) cm
f = -17 * 32/15 cm

Now we know the focal length of the convex mirror. To find the distance of the image when the object is 24 cm in front of the mirror, we can rearrange the mirror equation as follows:

1/dᵢ = 1/f - 1/d₀

Plugging in the values:

1/dᵢ = -15/(17 * 32) cm - 1/24 cm

Now, we can solve for dᵢ:

1/dᵢ = (-15/(17 * 32) * 24 - 1)/24 cm
1/dᵢ = (-15 * 24 - 17 * 32)/(17 * 32 * 24) cm
1/dᵢ = (-360 - 544)/(17 * 32 * 24) cm
1/dᵢ = -904/(17 * 32 * 24) cm
dᵢ = (17 * 32 * 24)/904 cm

Now we can simplify and calculate the result:

dᵢ = (544)/904 cm
dᵢ ≈ 0.6027 cm

Therefore, when the object is 24 cm in front of the mirror, the image is located approximately 0.6027 cm behind the mirror.