Optics 6 Question 6

7. The focal lengths of the objective and the eyepiece of a compound microscope are 2.0cm and 3.0cm respectively. The distance between the objective and the eyepiece is 15.0cm. The final image formed by the eyepiece is at infinity. The two lenses are thin. The distance in cm of the object and the image produced by the objective, measured from the objective lens, are respectively

(a) 2.4 and 12.0

(b) 2.4 and 15.0

(c) 2.0 and 12.0

(d) 2.0 and 3.0

(1995,2M)

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Answer:

Correct Answer: 7. (d)

Solution:

  1. Let intensity of each wave is I0.

Then, intensity at the centre of bright fringe will be 4I0.

Given, path difference, Δx=λ/8

Phase difference, φ=Δx×2πλ

φ=λ8×2πλ or φ=π/4

Intensity of light at this point,

I=I0+I0+2I0cos(π/4)=2I0+2I0=3.41I0

Now,

I4I0=3.414=0.85



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