Optics and Lenses, please draw the diagram and solve for a and b. Consider a sph

Question

Optics and Lenses, please draw the diagram and solve for a and b.

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. 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. 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 lens :

f = - 20 cm

do = object distance = 20 cm

di = image distance

using the lens equation

1/di + 1/do = 1/f

1/di + 1/20 = 1/-20

di = - 10 cm

ho = height of object = 5 cm

hi/ho = - di/do

hi/5 = - (- 10)/20

hi = 2.5

for the mirror :

do = object distance = 45 - 10 = 35 cm

di = image distance

f = focal length = 100 cm

using the mirror equation

1/f = 1/di + 1/do

1/100 = 1/di + 1/35

di = - 53.85 cm

ho = height of object = 2.5 cm

hi/ho = - di/do

hi/2.5 = - (- 53.85)/35

hi = 3.85 cm

the image is virtual , upright ,

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