A compound microscope has lenses of focal length 1.0cm and 5.0cm.an object is placed 1.2cm from the objective lens.if a virtual image is formed 25cm from the eyepiece,calculate the distance between the two lenses
To calculate the distance between the two lenses in the compound microscope, we can use the lens formula:
1/f = 1/v + 1/u
where
f = focal length of the lens
v = image distance
u = object distance
Let's first calculate the image distance from the objective lens:
1/1 = 1/25 + 1/1.2
1 = 0.04 + 0.8333
1 = 0.8733
Therefore, the image distance from the objective lens is 1/0.8733 ≈ 1.14 cm.
Now, let's calculate the object distance from the eyepiece:
1/5 = 1/25 + 1/u
0.2 = 0.04 + 1/u
0.16 = 1/u
u = 1/0.16 = 6.25 cm
Now, let's calculate the image distance from the eyepiece:
1/20 = 1/25 + 1/6.25
0.05 = 0.04 + 0.16
0.05 = 0.2
Therefore, the image distance from the eyepiece is 1/0.2 = 5 cm.
Finally, the distance between the two lenses is the sum of the image distance from the objective lens and the object distance from the eyepiece:
Distance between two lenses = 1.14 cm + 6.25 cm = 7.39 cm
Therefore, the distance between the two lenses in the compound microscope is 7.39 cm.