Two converging lenses having focal lengths of f_1 = 10.0 cm and f_2 = 20.0 cm ar

Question

Two converging lenses having focal lengths of f_1 = 10.0 cm and f_2 = 20.0 cm are positioned 60.0 cm apart. An object is placed 30.0 cm to the left of the first lens. A diagram tracing the rays is shown below. (i) Find the location (relative the first lens) and magnification of the object after going through the first (ii) Find the final location (relative to the second lens) and magnification of the object after going through the first lens. (iii) Is the final image real or virtual? Show your work. (iv) ls the final image magnified (larger) or diminished (smaller)? Show your work. (v) Is the final image upright or inverted? Show your work.

Explanation / Answer

part i.

for first lens:
object distance=u=-30 cm

focal length=f=10 cm

if image distance is v,

using thin lens equation,

(1/v)-(1/u)=1/f

==>1/v=(1/10)-(1/30)

==>v=15 cm

so image after first lens is 15 cm to the right of first lens.

magnification=v/u=15/(-30)=-0.5

part ii.

for the second lens:

object distance=u=-(60-15)=-45 cm

focal length=f=20 cm

if image distance is v,

(1/v)-(1/u)=1/f

==>v=36 cm

so final image is located 36 cm right of the second lens.

magnification due to second lens=36/(-45)=-0.8

total magnification=-0.5*(-0.8)=0.4

part iii.

final image is real as it forms to the right of the second lens.

part iv.

final image is smaller as magnification is less than 1.

part v:

final image is upright as magnification is positive.

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