A) Step 1: Draw diagram of compound microscope.
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/1531375/original_6.png)
Step 2: Find the object distance for the eyepiece.
Given: Focal length of the objective lens,
f0=2.0 cm
Focal length of the eyepiece,
fe=6.25 cm
Distance between the objective lens and the eyepiece,
d=15 cm
Using lens formula for the eyepiece,
1ve−1ue=1fe
1ue=1ve−1fe
1ue=1−25−16.251ue=−1−425=−15cm⇒ue=−5 cm
Step 3: Find the image distance for the objective lens.
Now the image distance for the objective lens is,
vo=d−|ue|
vo=15−5
vo=10cm
Step 4: Find the object distance for the objective lens.
Using lens formula for the eyepiece,
1vo−1uo=1f0
1uo=1vo−1f0
1uo=110−12
1uo=1−510=−410
uo=−2.5cm
Step5:Find the Magnification power of microscope.
Magnification of microscope at the least distance of distinct vision is given by,
m=vo|uo|(1+Dfe)
m=102.5(1+256.25)
m=4×5
m=20
Final Answer:
ue=−5cm
vo=10 cm
uo=−2.tcm
m=20.
B) Step 1: Draw diagram of compound microscope.
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/1531376/original_7.png)
Step 2: Find the object distance for the eyepiece.
Given:
Focal length of the objective lens,
f0=2.0 cm
Focal length of the eyepiece,
fe=6.25 cm
Distance between the objective lens and the eyepiece,
d=15 cm
Using lens formula for the eyepiece,
1ve−1ue=1fe
1ue=1ve−1fe
1ue=1∞−16.25
ue=−6.25 cm
Step 3: Find the image distance for the objective lens.
Now the image distance for the objective lens is,
vo=d−|ue|
vo=15−6.25
vo=8.75cm
Step 4: Find the object distance for the objective lens.
Using lens formula for the objective,
1vo−1uo=1fo
1uo=1vo−1fo
1uo=18.75−12
1uo=2−8.7517.5=−6.7517.5
uo=−2.59cm
Step5: Find the Magnification power of microscope.
Magnification of microscope at the least distance of distinct vision is given by,
m=vo|uo|(Dfe)
m=8.752.59(256.25)
m=13.51
Final Answer:
ue=−2.59cm
m=13.51.