A person with a normal near point (25 cm) using a compound microscope with objective of focal length 8.0 mm and an eyepiece of focal length 2.5 cm can bring an object placed at 9.0 mm from the objective in sharp focus. What is the separation between the two lenses? Calculate the magnifying power of the microscope,
Focal length of the objective lens, fo = 8 mm = 0.8 cm
Focal length of the eyepiece, fe = 2.5 cm
Object distance for the objective lens, uo = −9.0 mm = −0.9 cm
Least distance of distant vision, d = 25 cm
Image distance for the eyepiece, ve = −d = −25 cm
Object distance for the eyepiece $=u_{\mathrm{e}}$
Using the lens formula, we can obtain the value of $u_{\mathrm{e}}$ as:
\frac{1}{v_{e}}-\frac{1}{u_{e}}=\frac{1}{f_{e}}
$\frac{1}{u_{\mathrm{e}}}=\frac{1}{v_{\mathrm{e}}}-\frac{1}{f_{\mathrm{e}}}$
$=\frac{1}{-25}-\frac{1}{2.5}=\frac{-1-10}{25}=\frac{-11}{25}$
$\therefore u_{\mathrm{e}}=-\frac{25}{11}=-2.27 \mathrm{~cm}$
We can also obtain the value of the image distance for the objective lens $\left(v_{o}\right)$ using the lens formula.
$\frac{1}{v_{\mathrm{o}}}-\frac{1}{u_{\mathrm{o}}}=\frac{1}{f_{\mathrm{o}}}$
$\frac{1}{v_{\mathrm{o}}}=\frac{1}{f_{\mathrm{o}}}+\frac{1}{u_{\mathrm{o}}}$
$=\frac{1}{0.8}-\frac{1}{0.9}=\frac{0.9-0.8}{0.72}=\frac{0.1}{0.72}$
$\therefore v_{\mathrm{o}}=7.2 \mathrm{~cm}$
The distance between the objective lens and the eyepiece $=\left|u_{\mathrm{c}}\right|+v_{\mathrm{o}}$
$=2.27+7.2$
$=9.47 \mathrm{~cm}$
The magnifying power of the microscope is calculated as:
$\frac{v_{\mathrm{o}}}{\left|u_{\mathrm{o}}\right|}\left(1+\frac{d}{f_{\mathrm{e}}}\right)$
$=\frac{7.2}{0.9}\left(1+\frac{25}{2.5}\right)=8(1+10)=88$
Hence, the magnifying power of the microscope is 88.
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- JEE Main
- Exam Pattern
- Previous Year Papers
- PYQ Chapterwise
- Physics
- Kinematics 1D
- Kinemetics 2D
- Friction
- Work, Power, Energy
- Centre of Mass and Collision
- Rotational Dynamics
- Gravitation
- Calorimetry
- Elasticity
- Thermal Expansion
- Heat Transfer
- Kinetic Theory of Gases
- Thermodynamics
- Simple Harmonic Motion
- Wave on String
- Sound waves
- Fluid Mechanics
- Electrostatics
- Current Electricity
- Capacitor
- Magnetism and Matter
- Electromagnetic Induction
- Atomic Structure
- Dual Nature of Matter
- Nuclear Physics
- Radioactivity
- Semiconductors
- Communication System
- Error in Measurement & instruments
- Alternating Current
- Electromagnetic Waves
- Wave Optics
- X-Rays
- All Subjects
- Physics
- Motion in a Plane
- Law of Motion
- Work, Energy and Power
- Systems of Particles and Rotational Motion
- Gravitation
- Mechanical Properties of Solids
- Mechanical Properties of Fluids
- Thermal Properties of matter
- Thermodynamics
- Kinetic Theory
- Oscillations
- Waves
- Electric Charge and Fields
- Electrostatic Potential and Capacitance
- Current Electricity
- Thermoelectric Effects of Electric Current
- Heating Effects of Electric Current
- Moving Charges and Magnetism
- Magnetism and Matter
- Electromagnetic Induction
- Alternating Current
- Electromagnetic Wave
- Ray Optics and Optical Instruments
- Wave Optics
- Dual Nature of Radiation and Matter
- Atoms
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