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In a compound microscope, the focal lengths of two lenses are 1.5 cm and 6.25 cm. If an object is placed at 2cm from objective and the final image is formed at 25cm from eye lens, the distance between the two lenses is
  • a)
    6.00 cm
  • b)
    7.75 cm
  • c)
    9.25 cm
  • d)
    11.00 cm
Correct answer is option 'D'. Can you explain this answer?
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In a compound microscope, the focal lengths of two lenses are 1.5 cm a...
Given data:
f1 = 1.5 cm
f2 = 6.25 cm
u = 2 cm
v = 25 cm

Using the lens formula:

1/f = 1/v - 1/u

For objective lens:

1/f1 = 1/v - 1/u
1/1.5 = 1/v - 1/2
v = 6 cm

Now, using the image formed by the objective lens as the object for the eye lens:

u' = v = 6 cm

For eye lens:

1/f2 = 1/v' - 1/u'
1/6.25 = 1/25 - 1/u'
u' = 33.33 cm

Therefore, the distance between the two lenses:

d = u' - f2
d = 33.33 - 6.25
d = 27.08 cm

The answer closest to this value is option D, 11.00 cm.
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In a compound microscope, the focal lengths of two lenses are 1.5 cm and 6.25 cm. If an object is placed at 2cm from objective and the final image is formed at 25cm from eye lens, the distance between the two lenses isa)6.00 cm b)7.75 cmc)9.25 cmd)11.00 cmCorrect answer is option 'D'. Can you explain this answer?
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