Two-lens systems. The stick figure O (the object) stands on the common central a

Question

Two-lens systems. The stick figure O (the object) stands on the common central axis of two thin, symmetric lenses. Lens 1 is mounted within the boxed region closer to O, which is at object distance d0 1. Lense 2 is mounted within the farther boxed region, at distance d. The table refers to the focal distances f1 and f2 for lens 1 and lens 2 respectively, the image distance di2 for the final image produced by lens 2 (the final image produced by the system) and the overall lateral magnification m_tot for the system. All distance are in centimeters. Fill in the missing information, including signs.

Explanation / Answer

A)

image due to first lense1

object distance u=12 cm

focal lemgth f1=7.5 cm

let image distance be v

1/u+1/v=1/f1

1/12+1/v=1/7.5

===>

v=20cm, this is the image due to first lense1

separation between lens1 and lens2 is d=32 cm

now,

object distance for the second lense2 is,

u'=32-20

u'=12cm

let image distnace be v'

and

focal length of lense B is, f2=6cm

now,

1/u'+1/v'=1/f2

1/12+1/v'=1/(6)

===> v'=12 cm

v'=12 cm

image distance due to second lense is v'=12 cm ( from the lense2)

now,

final image distance from the actual object is d_i2=(12+32+12)=56cm ( from the actual object)

or

final image position from the first lense is =30+12=42cm

B)

total magnification M=m1*m2

here,

magnificatin of first lense is m1=v/u=20/12=1.67

magnificatin of second lense is m2=12/12=1

now,

M=m1*m2

M=1.67*1

M=1.67

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