A concave spherical mirror has a radius of curvature of 14.0 cm . A.) Calculate

Question

A concave spherical mirror has a radius of curvature of 14.0 cm .

A.) Calculate the location of the image formed by an 14.0-mm-tall object whose distance from the mirror is 28.0 cm .

Calculate the size of the image.

B.) Calculate the location of the image formed by an 14.0-mm-tall object whose distance from the mirror is 14.0 cm .

Calculate the size of the image.

C.) Calculate the location of the image formed by an 14.0-mm-tall object whose distance from the mirror is 3.50 cm .

Calculate the size of the image.

D.) Calculate the location of the image formed by an 14.0-mm-tall object whose distance from the mirror is 10.0 m .

Calculate the size of the image.

Explanation / Answer

Let:
u be the object distance,
v be the image distance,
r be the radius of curvature,
f be the focal length,
m be the magnification,
H be the image height,
h be the object height.

The equations I use are:
1 / u + 1 / v = 2 / r = 1 / f
m = v / u
H = mh = vh / u
with f and r positive for a concave mirror, and negative for a convex mirror.

A)
1 / 28 + 1 / v = 2 / 14
1 / v = 1 / 7 - 1 / 28
v = 9.334 cm.

H = vh / u
= 9.334 * 14.0 / 28 = 4.667 cm

That's an inverted, real image in front of the mirror.

B)

1 / 14 + 1 / v = 2 / 14
1 / v = 1 / 7 - 1 / 14
v = 14 cm.

H = vh / u
= 14 * 14.0 / 14 = 14 cm

That's an inverted, real image in front of the mirror.

C)

1 / 3.5 + 1 / v = 2 / 14
1 / v = 1 / 7 - 1 / 14
v = -7 cm.

H = vh / u
= -7 * 14.0 / 3.5 = 28 cm

That's an erect, virtual image behind the mirror.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.