Two thin lenses with a focal length of magnitude 13.5 cm , the first diverging a

Question

Two thin lenses with a focal length of magnitude 13.5 cm , the first diverging and the second converging, are located 10.1 cm apart. An object 1.60 mm tall is placed 22.5 cm to the left of the first (diverging) lens.

Part A: How far from this first lens is the final image formed? Express your answer in centimeters to three significant figures. (unit in cm)

Part B

Is the final image real or virtual?

Part C

What is the height of the final image?

Express your answer in millimeters to three significant figures. (unit in mm)

Part D

Is it upright or inverted?

Explanation / Answer

FOr first lens,

f1 = - 13.5 cm

Object distance, p1 = 22.5 cm

Applying lens equation,

1/f1 = 1/p1 + 1/q1

1/(-13.5) = 1/22.5 + 1/q1

q1 = - 8.44 cm

now this image will act as object for second lens,

object distance for lens 2, p2 = 8.44 + 10.1 = 18.54 cm

f2 = 13.5 cm

1/13.5 = 1/18.54 + 1/q2

q2 = 49.7 cm

so final image is 49.7 + 10.1 = 59.8 cm right to the first lens.

(B) Image is real.

(C) M = ( - q1 / p1)(- q2 / p2)

= (- 8.44 / 22.5) ( 49.7 / 18.54)

= - 1

so height of image is 1.60 mm.

(D) M is negative so image is inverted.

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