How do I find the height of the image?

[phys62]

Homework Statement

A 1.80-cm-high object is situated 19.7 cm in front of a concave mirror that has a radius of curvature of 12.2 cm. Calculate (a) the location and (b) the height of the image.

Homework Equations

f=1/2R
1/image distance + 1/object distance = 1/f

The Attempt at a Solution

f=1/2(12.2) = 11.1
1/image distance + 1/19.7 = 1/6.1
image distance = 8.836 cm

then I thought to find the image height I'd just take 8.836 cm - 1.8 cm = 7.036 cm but this is incorrect.

 

[jambaugh]

The ratio of image height to object height = the magnification will equal the ratio of distance from image over distance of the object to the mirror or lens.

 

[nlightner]

To accurately find the height of the image, we need to use the magnification formula: m = -di/do = hi/ho, where m is the magnification, di is the image distance, do is the object distance, hi is the image height, and ho is the object height.

Firstly, we can calculate the image distance (di) using the mirror equation: 1/di + 1/19.7 = 1/11.1. This gives us a di value of 6.68 cm.

Next, we can use the magnification formula to find the image height (hi): m = -6.68/19.7 = hi/1.80. Solving for hi, we get a value of -0.61 cm.

Since the image is virtual (formed behind the mirror), the negative sign indicates that the image is upright, and the magnitude (0.61 cm) represents the height of the image.

Therefore, the height of the image is 0.61 cm.