Optics 7 Question 6

6. Two identical glass rods S1 and S2 (refractive index =1.5 ) have one convex end of radius of curvature 10cm. They are placed with the curved surfaces at a distance d as shown in the figure, with their axes (shown by the dashed line) aligned. When a point source of light P is placed inside rodS1 on its axis at a distance of 50cm from the curved face, the light rays emanating from it are found to be parallel to the axis inside S2. The distance d is

(2015 Adv.)

(a) 60cm

(b) 70cm

(c) 80cm

(d) 90cm

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Solution:

  1. R=10cm

Applying μ2vμ1u=μ2μ1R two times

1v1.550=11.5101v+1.550=0.5101v=0.5101.550=2.51.550v=50MN=d,MI1=50cm,NI1=(d50)cm

 Again, 1.51(d50)=1.51101d50=120d=70



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