# An Angular Magnification (Magnifying Power) of 30x is Desired Using an Objective of Focal Length 1.25 Cm and an Eyepiece of Focal Length 5 Cm. How Will You Set up the Compound Microscope? - Physics

Numerical

An angular magnification (magnifying power) of 30X is desired using an objective of focal length 1.25 cm and an eyepiece of focal length 5 cm. How will you set up the compound microscope?

#### Solution

Focal length of the objective lens, fo = 1.25 cm

Focal length of the eyepiece, fe = 5 cm

Least distance of distinct vision, d = 25 cm

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")

= (1 + 25/5)

= 6

The angular magnification of the objective lens (mo) is related to me as:

mo me = m

mo = "m"/"m"_"e"

= 30/6

= 5

We also have the relation:

"m"_"o" = ("Image distance for the objective lens" ("v"_"o"))/("Object distance for the objective lens" (-"u"_"o"))

5 = "v"_"o"/-"u"_"o"

∴ vo = −5uo ................(1)

Applying the lens formula for the objective lens:

1/"f"_"o"  = 1/"v"_"o" - 1/"u"_"o"

1/1.25  = 1/(-5"u"_"o") - 1/"u"_"o"

= (-6)/(5"u"_"o")

∴ "u"_"o" = (-6)/5 xx 1.25 = −1.5 cm

And vo = −5uo

= −5 × (−1.5) = 7.5 cm

The object should be placed 1.5 cm away from the objective lens to obtain the desired magnification.

Applying the lens formula for the eyepiece:

1/"v"_"e" - 1/"u"_"e" = 1/"f"_"e"

Where,

ve = Image distance for the eyepiece = −d = −25 cm

ue = Object distance for the eyepiece

1/"u"_"e" = 1/"v"_"e" - 1/"f"_"e"

= (-1)/25 - 1/5

= - 6/25

∴ ue = −4.17 cm

Separation between the objective lens and the eyepiece = |"u"_"e"| + |"v"_"o"|

= 4.17 + 7.5

= 11.67

Therefore, the separation between the objective lens and the eyepiece should be 11.67 cm.

Concept: Optical Instruments - The Microscope
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#### APPEARS IN

NCERT Physics Part 1 and 2 Class 12
Chapter 9 Ray Optics and Optical Instruments
Exercise | Q 9.27 | Page 347
NCERT Class 12 Physics Textbook
Chapter 9 Ray Optics and Optical Instruments
Exercise | Q 33 | Page 349

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