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# Solution - 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? - CBSE (Science) Class 12 - Physics

ConceptThe Microscope

#### Question

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,f_o = 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:

m_om_e = m

m_o = 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

:. v_o =  -5u_o   ....(1)

Applying the lens formula for the objective lens:

1/f_o  = 1/v_o - 1/u_o

1/1.25  = 1/(-5u_o) - 1/u_o = (-6)/(5u_o)

:. u_o = -6/5   xx  1.25 = - 1.5 cm

And v_o = -5u_o

= -5xx(-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,

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

u_e = Object distance for the eyepiece

1/u_e = 1/v_e - 1/f_e

= (-1)/25 - 1/5 = - 6/25

:. u_e = -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.

Is there an error in this question or solution?

#### APPEARS IN

NCERT Physics Textbook for Class 12 Part 2 (with solutions)
Chapter 9: Ray Optics and Optical Instruments
Q: 33 | Page no. 349

#### Reference Material

Solution for question: 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? concept: null - The Microscope. For the courses CBSE (Science), CBSE (Commerce), CBSE (Arts)
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