Question

A concave spherical mirror has a radius of curvature of 15.0 cm .

a) Calculate the size of the image formed by an 7.00 mm -tall object whose distance from the mirror is 30.0 cm . Express your answer in millimeters to three significant figures.

b) Calculate the location of the image formed by an 7.00 mm -tall object whose distance from the mirror is 15.0 cm . Express your answer in centimeters to three significant figures.

c) Calculate the location of the image formed by an 7.00 mm -tall object whose distance from the mirror is 3.75 cm . Express your answer in centimeters to three significant figures.

d) Calculate the location of the image formed by an 7.00 mm -tall object whose distance from the mirror is 10.0 m . Express your answer in centimeters to three significant figures.

Answer 1

f = R/2 = 7.5 cm

1/f = 1/p + 1/q

(A) p = 30 cm

1/7.5 = 1/30 + 1/q

q = 10 cm

m = -q / p = hi / ho

- 10 / 30 = hi / 7

hi = - 2.33 mm

(minus sign means image is inverted)

(B) p = 15 cm

1/7.5 = 1/15 + 1/q

q = 15 cm

m = -q / p = hi / ho

- 15 / 15 = hi / 7

hi = - 7 mm

(minus sign means image is inverted)

(C) p = 3.75 cm

1/7.5 = 1/3.75 + 1/q

q = -7.5 cm

m = -q / p = hi / ho

- (-7.5) / 3.75 = hi / 7

hi = 14 mm

  

(D)

p = 1000 cm

1/7.5 = 1/1000 + 1/q

q = 7.557cm

m = -q / p = hi / ho

- 7.557 / 1000 = hi / 7

hi = - 0.0529 mm

(minus sign means image is inverted)