An angular magnification of 30x is desired using an objective of focal length 1.25cm and an eyepiece of focal length 5cm .How will you set up the compound microscope ?
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Ray Optics and Optical Instruments
Optical Instruments : Microscope
An angular magnification (m...
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Asked on November 22, 2019 by
Ranjana Duvvuru
An angular magnification (magnifying power) of 30X is desired using an objective of focal length 1.25cm and an eyepiece of focal length 5cm. How will you set up the compound microscope?
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ANSWER
Focal length of the objective lens, f
o
=1.25cm
Focal length of the eyepiece, f
e
=5cm
Least distance of distinct vision, d=25cm
Angular magnification of the compound microscope = 30X
Total magnifying power of the compound microscope, m=30
The angular magnification of the eyepiece is given by the relation-
m
e
=(1+d/f
e
)=6
The angular magnification of the objective lens (m
o
) is calculated as-
m
o
m
e
=m⇒m
o
=5
Now, m
o
=−v
o
/u
o
⇒v
o
=−5u
o
Using lens formula,
v
o
1
−
u
o
1
=
f
o
1
Using above two equations, u
o
=−1.5cm and v
o
=7.5cm
So, The object should be placed 1.5 cm away from the objective lens to obtain the desired magnification.
Now, Image distance for the eyepiece is v
e
=−d=−25cm
Using lens formula,
v
e
1
−
u
e
1
=
f
e
1
u
e
=−4.17cm
Separation between the objective lens and the eyepiece, ∣u
e
∣+∣v
o
∣=11.67cm
Therefore, the separation between the objective lens and the eyepiece should be 11.67cm.