Optics 6 Question 7

8. An astronomical telescope has an angular magnification of magnitude 5 for far objects. The separation between the objective and the eyepiece is 36cm and the final image is formed at infinity. The focal length fo of the objective and the focal length fe of the eyepiece are

(1989, 2M)

(a) fo=45cm and fe=9cm

(b) fo=50cm and fe=10cm

(c) fo=7.2cm and fe=5cm

(d) fo=30cm and fe=6cm

Objective Question II (One or more correct option)

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Solution:

  1. In the given case, figure for first minima will be as shown below

We know that condition for minima in Young’s double slit experiment is path difference,

 For first minima, n=1Δx=λ/2

Path difference between the rays coming from virtual sources S1 and S2 at point ’ P ’ will be

Δx=S2PS1P

From triangle S1S2P,

S1P=2d

and (S2P2)=(S1S2)2+(S1P)2=d2+(2d)2

(S2P2)=5d2 or S2P=5d

Substituting the values from Eqs. (iii) and (iv) in Eq. (ii), we get

Δx=5d2d

From Eqs. (i) and (v), we get

5d2d=λ/2d=λ2(52)



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