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.