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

Answer 1

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.