Consider a spherical mirror and lens separated by 45 cm. The mirror is on the le
ID: 1455162 • Letter: C
Question
Consider a spherical mirror and lens separated by 45 cm. The mirror is on the left with a focal length of 100 cm. The lens is on the right with a focal length of 20 cm. A 5 cm tall object is placed 20 cm to the left of the lens.
a) If you only consider the rays that move to the right from the object, fully characterize the final image in the system. In other words provide final image location, real/virtual, upright/inverted, final magnification, and final image height.
b) If you only consider the rays that move to the left from the object, fully characterize the final image in the system. In other words provide final image location, real/virtual, upright/inverted, final magnification, and final image height.
Explanation / Answer
a)
for mirror
object distance s1 = 45-20 = 25 cm
image distance = s1' = ?
focal length f1 = 100 cm
1/s1 + 1/s1' = 1/f1
1/25 + 1/s1' = 1/100
s1' = -33.33 cm
magnification m1 = -s1'/s1 = 33.33/25
m1 = 1.3332
for lens
s2 = 45 + 33.33 = 78.33 cm
f2 = -20 cm
1/s2 + 1/s2' = 1/f2
1/78.33 + 1/s2' = -1/20
s2' = -16 cm
m2 = -s2'/s2 = 16/78.33 = 0.204
final image is 16 cm to the left of the lens
image is virtual
image is upright
M = m1*m2 = 1.3332*0.204 = 0.272
hi = M*ho = 0.272*5 = 1.36 cm
+++++++++++++++++++++++++++++++++
for lens
object distance s1 = 20 cm
image distance = s1' = ?
focal length f1 = -20 cm
1/s1 + 1/s1' = 1/f1
1/20 + 1/s1' = -1/20
s1' = -10 cm
magnification m1 = -s1'/s1 = 10/20 = 0.5
for mirror
s2 = 45 -10 = 35 cm
f2 = 100 cm
1/s2 + 1/s2' = 1/f2
1/35 + 1/s2' = 1/100
s2' = -53.8 cm
m2 = -s2'/s2 = 53.8/35 = 1.54
final image is 53.8 cm to the left of the mirror
image is virtual
image is upright
M = m1*m2 = 0.5*1.54 = 0.77
hi = M*ho = 0.77*5 = 3.85 cm