A thin, converging lens having a focal length of magnitude 24.00 cm is placed 1.

Question

A thin, converging lens having a focal length of magnitude 24.00 cm is placed 1.000 m from a plane mirror that is oriented perpendicular to the principal axis of the lens. A flower, 8.400 cm tall, is 1.60 m from the mirror on the principal axis of the lens.

1)Where is the final image of the flower produced by the lens–mirror combination? Enter the image distance with respect to the mirror. Follow the sign convention.

2) How tall is the image? Follow the sign convention.

3) If the converging lens is replaced by a diverging lens having a focal length of the same magnitude as the original lens, where is the final image of the flower produced by the lens-mirror combination? Enter the image distance with respect to the mirror. Follow the sign convention.

Explanation / Answer

1)

f1=24cm, do1=60cm=100,f2= infinity

For converging lens,

1/f1=1/do1+1/di1

1/24=1/60+1/di1

di1= 40cm

Positive sign indicates that image flower from the converging lens is opposite side of the lens and hence real and is 40cm from the lens.

m1=-di1/do1 = hi1/ho1

m1=-40cm/60cm = -2/3 = = -0.67

hi1= m1*ho1= -0.67*8.4cm = -5.628cm

since the lens is 100cm from the mirror and to the left of the mirror.

Image is di1 is (100cm -40cm) = 60cm from the mirror.

Thus do2= 60cm

Plugging values,

1/f2=1/do2+1/di2

1/infinity = 1/60cm +1/di2

di2 = -60cm

This is the final image of lens-mirror combination.

Thus final image di2=-60cm and inverted thus virtual.

2)

Negative sign indicates image is opposite side of the mirror and hence real.

m2=-di2/do2 = hi2/ho2 = -(-60cm)/60cm = +1

hi2=m2*ho1 = 1=1*--5.628cm = -5.826cm

3)

when f1=-24cm

For converging lens,

1/f1=1/do1+1/di1

-1/24=1/60+1/di1

di1=-17.14cm

Negative sign indicates image is to object side.

m1=-di1/do1 = -(-17.14)/60 = 0.29

hi1= m1*ho1 = 0.29*8.4cm = 2.44cm

Positive sign indicates image is upright.

Hence do2= 100cm + 17.14cm = 117.14cm

For mirror,

1/f2=1/do2+1/di2

1/0 = 1/117.14 +1/di2

di2= -117.14

Final image di2 is 177.14cm from the plane mirror and into the mirror/opposite side of the mirror.

Image di2 is upright is hi1 is upright.

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