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Question

Two identical glass rods S1 and S2 (refractive index = 1.5) have one convex end of radius of curvature 10 cm. 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 rod S1 on its axis at a distance of 50 cm from the curved face, the light rays emanating from it are found to be parallel to the axis inside S2. The distance d is:
1010993_a98d921fd7c8430da02fe3c46d2782aa.png
  1. 60 cm
  2. 70 cm
  3. 80 cm
  4. 90 cm

A
80 cm
B
90 cm
C
60 cm
D
70 cm
Solution
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Applying (μ2vμ1u=μ2μ1R) two times, we will get
1v1.550=11.510
1v=0.5101.550=2.51.550
v=50.
AB=d, AI1=50cm BI1=(d50)cm

Again, 1.51(d50)=1.5110
1d50=120
d=70cm.
Hence, the answer is 70cm.

1103448_1010993_ans_14d322755eef4ad589513c5ad9bd4d07.png

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