A person with a normal near point(25cm)using a compound microscope with an objective of focal length 8.0mm and an eyepiece of focal length 2.5cm can bring an object placed at 9.0mm from the objective in sharp focus. What is the separation between the two lenses? Calculate the magnifying power of the microscope.
A person with a normal near point(25cm)using a compound microscope with an objective of focal length 8.0mm and an eyepiece of focal length 2.5cm can bring an object placed at 9.0mm from the objective in sharp focus. What is the separation between the two lenses? Calculate the magnifying power of the microscope.
Solution and Explanation
Focal length of the objective lens,f0=8mm=0.8cm
Focal length of the eyepiece,fe=2.5cm
Object distance for the objective lens,uo=-9.0mm=-0.9cm
Least distance of the eyepiece,ve=-d=-25cm
Object distance for the eyepiece=ue
Using the lens formula, we can obtain the value of ue as:\(\frac{1}{v_e}-\frac{1}{u_e}=\frac{1}{f_e}\)
\(\frac{1}{u_e}=\frac{1}{v_e}-\frac{1}{f_e}\)
=\(\frac{1}{-25}-\frac{1}{2.5}\)
=-\(1-\frac{10}{25}\)
=\(-\frac{11}{25}\)
∴\(u_e=-\frac{25}{11}\)=-2.27cm
We can also obtain the value of the image distance for the objective lens(vº)using the lens formula.
\(\frac{1}{v_e}-\frac{1}{u_e}=\frac{1}{f_e}\)
=\(\frac{1}{0.8}-\frac{1}{0.9}\)
=\(\frac{0.9-0.8}{0.72}\)
=\(\frac{0.1}{0.72}\)
The distance between the objective lens and the eyepiece=|ue|+vº=2.27+7.2=9.47cm
The magnifying power of the microscope is calculated as
\(\frac{v_e}{|u_e|}(1+\frac{d}{f_e})\)=\(\frac{7.2}{0.9}(1+\frac{25}{2.5})\)=8(1+10)=88
Hence, the magnifying power of the microscope is 88.
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Concepts Used:
Ray Optics and Optical Instruments
Optics, deals with the determination of behaviour and the properties of light, along with its interactions with the matter and also with the instruments that are used to detect it.
Ray optics is also known as the geometrical optics and it is a branch of science which describes light propagation.
Reflection is the change in direction of light at an interface in-between two different media so that the wave-front returns into a medium from which it was originated.
Speed of light is the rate at which the light travels in free space.
A phenomenal change in image formed when the light is passed from one medium to another which is called Refraction.
Total Internal Reflection is the reflection of light when the light ray enters into a rarer medium from a denser medium and the angle of incidence is higher than the critical angle of incidence then that light ray will be reflected back to the denser medium.
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