A concave makeup mirror is designed so that

a person 25.3 cm in front of it sees an upright
image at a distance of 54.0 cm behind the
mirror.
a) What is the radius of curvature of the
mirror?
Answer in units of cm

do=25.3cm

di=54.0cm
find f using following equation:

1/do + 1/di = 1/f

f=r/2

so the radius is 2 times the focal length

To find the radius of curvature of the concave mirror, you can use the mirror formula:

1/f = 1/v - 1/u

Where:
f is the focal length of the mirror,
v is the image distance (distance of the image from the mirror),
u is the object distance (distance of the object from the mirror).

In this case, the person is 25.3 cm in front of the mirror, so u = -25.3 cm (negative because it is in front of the mirror). The person sees an upright image at a distance of 54.0 cm behind the mirror, so v = 54.0 cm.

Plugging these values into the mirror formula:

1/f = 1/54.0 - 1/-25.3

Simplifying this equation:

1/f = (25.3 - 54.0) / (54.0 * -25.3)

Calculating the value of 1/f:

1/f = -28.7 / (-1362.2)

1/f = 0.0211

Now, to find the radius of curvature (R), the formula is:

R = 2f

Substituting the value of f into this equation:

R = 2 * 0.0211

R = 0.0422 cm

Therefore, the radius of curvature of the concave mirror is 0.0422 cm.

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