An object 1.99 cm high is placed 40.5 cm to the left of a converging lens having

Question

An object 1.99 cm high is placed 40.5 cm to the left of a converging lens having a focal length of 30.1 cm. A diverging lens with a focal length of 20.0 cm is placed 110 cm to the right of the converging lens.

(a) Determine the position of the final image.

(b) Determine the magnification of the final image.


(c) Is the image upright or inverted?

upright/inverted

(d) Repeat parts (a) through (c) for the case in which the second lens is a converging lens having a focal length of 20.0 cm.
final image location

magnification



Is the image upright or inverted?

distance . cm location ---Select--- to the right  to the left  of the diverging lens

Explanation / Answer

a)
given,
f1 = 30.1 cm

let u1 and v1 are the image and object distances for first lense

1/v1 + 1/u1 = 1/f1

1/v1 = 1/f1 - 1/u1

1/v1 = 1/30.1 - 1/40.5

v1 = 117.2 cm

image distnace for second lense, u2 = -117.2 + 110 = -7.2 cm

f2 = -20 cm

let v2 is the image distance for second lense.

Apply, 1/u2 + 1/v2 = 1/f2

1/v2 = 1/f2 - 1/u2

1/v2 = 1/(-20) - 1/(-7.5)

v2 = 12 cm to the right of the diverging lens <<<<<-----Answer

b)
magnification of first lense, m1 = -v1/u1

= -117.2/40.5

= -2.89

magnification of second lense, m2 = -v2/u2

= -12/(-7.2)

= 1.67

overall magnification, M = m1*m2

= -2.89*1.67

= -4.82

c)Image is inerted

d)

a)
given,
f1 = 30.1 cm

let u1 and v1 are the image and object distances for first lense

1/v1 + 1/u1 = 1/f1

1/v1 = 1/f1 - 1/u1

1/v1 = 1/30.1 - 1/40.5

v1 = 117.2 cm

image distnace for second lense, u2 = -117.2 + 110 = -7.2 cm

f2 = 20 cm

let v2 is the image distance for second lense.

Apply, 1/u2 + 1/v2 = 1/f2

1/v2 = 1/f2 - 1/u2

1/v2 = 1/(20) - 1/(-7.5)

v2 = 5.45 cm to the right of the diverging lens <<<<<-----Answer

b)
magnification of first lense, m1 = -v1/u1

= -117.2/40.5

= -2.89

magnification of second lense, m2 = -v2/u2

= -5.45/(-7.2)

= 0.757

overall magnification, M = m1*m2

= -2.89*0.757

= -2.2

c)Image is inerted

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