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Solution for 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

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
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: Optical Instruments - The Microscope. For the course CBSE (Science)
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