An object 3.60 cm tall is placed 13.1 cm in

front of a mirror, which creates an upright
image that is 5.21 cm in height.
a) What is the magnification of the image?
b) What is the radius of curvature of the
mirror?
Answer in units of cm

a) To find the magnification of the image, we can use the formula:

Magnification = Height of Image / Height of Object

Given that the height of the object (h_o) is 3.60 cm and the height of the image (h_i) is 5.21 cm, we can substitute them into the formula:

Magnification = 5.21 cm / 3.60 cm

Using a calculator, we can find that the magnification is approximately 1.447.

b) To find the radius of curvature of the mirror, we need to use the mirror formula:

1/f = 1/do + 1/di

where f is the focal length of the mirror, do is the object distance (distance of the object from the mirror), and di is the image distance (distance of the image from the mirror).

Since the object is placed in front of the mirror, the object distance (do) is positive, which is 13.1 cm. The image distance (di) is also positive because the image is on the same side as the object. However, we do not have the values for focal length or image distance, so we need to find di first.

Using the magnification formula, magnification = di / do, we can rearrange it to solve for di:

di = magnification * do

Substituting the given values, di = 1.447 * 13.1 cm, we can calculate di to be approximately 18.9357 cm.

Now that we have both do and di, we can substitute them into the mirror formula:

1/f = 1/13.1 cm + 1/18.9357 cm

To simplify this equation, we can convert the fractions to have a common denominator:

1/f = (18.9357 + 13.1) / (13.1 * 18.9357)

Simplifying further, we get:

1/f = 32.0357 / 247.85327

Now we can take the reciprocal of both sides to solve for f:

f = 247.85327 / 32.0357

Using a calculator, we can find that the radius of curvature of the mirror is approximately 7.74 cm.