A concave spherical mirror has a radius of curvature of 7.00 cm . a. Calculate t

Question

A concave spherical mirror has a radius of curvature of 7.00 cm .

a. Calculate the size of the image formed by an 14.0 mm -tall object whose distance from the mirror is 14.0 cm .

b. Calculate the size of the image formed by an 14.0 mm -tall object whose distance from the mirror is 7.00 cm . Express your answer in millimeters to three significant figures.

c. Calculate the size of the image formed by an 14.0 mm -tall object whose distance from the mirror is 1.75 cm .

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

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

Someone please help me. Show all work please.

Explanation / Answer

for concave spehrical mirroe

1/u + 1/v = 1/f = 2/R

or 1/v = 1/f - 1/u

part A :

1/v = 2/7 - 1/14

v = + 4.67 cm

manification M = -v/u = -4.67/14 = -0.3344

image size = u = Mu -0.3344 *14 = -4.67 mm

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

-------------------

part B :

1/v = 2/7 - 1/7

v = + 7 cm

manification M = -v/u = 7/7 = 1

image size = u = Mu = 1 *14 = 14 mm

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

part C :

1/v = 2/7 - 1/1.75

v = -3.5 cm

manification M = -v/u = -3.5/1.75 = -2

image size = u = Mu = -2*14 = -28 mm

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

part D

1/v = 2/7 - 1/10

v = + 5.38 cm

PART E

manification M = -v/u = -5.38/10 = -0.538

image size = u = Mu = 0.538 *14 = -7.5 mm

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

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