Visitors at a science museum are invited to sit in a chair to the right of a ful

Question

Visitors at a science museum are invited to sit in a chair to the right of a full-length diverging lens (f1 = -3.40 m) and observe a friend sitting in a second chair, 2.30 m to the left of the lens. The visitor then presses a button and a converging lens (f2 = +4.30 m) rises from the floor to a position 2.10 m to the right of the diverging lens, allowing the visitor to view the friend through both lenses at once. Find (a) the magnification of the friend when viewed through the diverging lens only and (b) the overall magnification of the friend when viewed through both lenses.

Explanation / Answer

a) for the first lense

f1 = -3.4 m

u1 = 2.3 m

let v1 is the image distance for the first lens

Apply,

1/u1 + 1/v1 = 1/f1

1/v1 = 1/f1 - 1/u1

1/v1 = 1/(-3.4) - 1/(2.3)

v1 = -1.37 m

magnification, m1 = -v1/u1

= -(-1.37)/2.3

= 0.596 <<<<<<<<<---------------Answer

b) for the second lens, f2 = +4.3 cm

object distance, u2 = 1.37 + 2.1

= 3.47 m

let v2 is the image distance from the seond lens

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

1/v2 = 1/f2 - 1/u2

1/v2 = 1/4.3 - 1/3.47

v2 = -17.98 m

magnification of second lens, m2 = -v2/u2

= -(-17.98)/3.47

= 5.2

overall magnification, M = m1*m2

= 0.596*5.2

= 3.1   <<<<<<<--------------Answer

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