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NCERT Class XII Chapter
Ray Optics and Optical Instruments
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Question : 12 of 38
Marks: +1, -0
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.
Solution:  
The image is formed at least distance of distinct vision for sharp focus. The separation between two lenses will be vo+∣ue∣v_o + \lvert u_e \rvert
Let us find first vov_o the image distance for objective lens.
1v0−1u0\frac{1}{v_0} - \frac{1}{u_0} = 1f0\frac{1}{f_0} or 1v0\frac{1}{v_0} - 1−9\frac{1}{-9} = 18\frac{1}{8} or 1v0\frac{1}{v_0} = 18−19\frac{1}{8} - \frac{1}{9} = 172\frac{1}{72}
⇒ v0v_0 = 72 mm = 7.2 cm
Also we can find object distance for eyepiece ueu_e, as we know
vev_e = D = 25 cm = 250 mm
1ve−1ue\frac{1}{v_e} - \frac{1}{u_e} = 1fe\frac{1}{f_e} ⇒ 1−250−1ue\frac{1}{-250} - \frac{1}{u_e} = 125−1ue\frac{1}{25} - \frac{1}{u_e} = 125+1250\frac{1}{25} + \frac{1}{250} = 10+1250\frac{10+1}{250}
ueu_e = - 25011\frac{250}{11} mm = - 22.7 mm = - 2.27 cm
Separation between lenses
L = vo+∣ue∣v_o + \lvert u_e \rvert = 72 + 22.7 or L = 94.7 mm = 9.47 cm
Magnifying power m = −v0u0[1+Dfe]-\frac{v_0}{u_0} \left[1 + \frac{D}{f_e}\right]
m = - 72−9[1+25025]\frac{72}{-9} \left[1 + \frac{250}{25}\right] = 8 [11] = 88
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